An athlete of mass 50kg in the Olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range:

A particle is projected at 60⁰ to the horizontal with a kinetic energy $K$. The kinetic energy at the highest point is:

If mass-­energy equivalence is taken into account, when water is cooled to form ice, the mass of water should

A ball whose kinetic energy is $E$,  is projected at an angle of $45^\circ$ to the horizontal. The kinetic energy of the ball at the highest point of its flight will be

 A spring of unstretched length l has a mass m with one end fixed to a rigid support. Assuming the spring to be made of a uniform wire, the kinetic energy possessed by it, if its free end is pulled with uniform velocity, $v$ is :

The average mass of raindrops is 3.0x10^-5 kg and their average terminal velocity is 9 m/s.  Calculate the energy transferred by rain to each square metre of the surface at a place which receives 100 cm of rain in a year.

Two particles of the same mass m are moving in circular orbits because of force, given by  The first particle is at a distance r=1, and the second, at r=4. The best estimate for the ratio of kinetic energies of the first and the second particle is closest to :

Consider the following two statements

A. The linear momentum of a system of particles is zero.

B. The kinetic energy of a system of particles is zero.

Then

A knife of mass m is dropped from height h on the ground . It penetrate the block from distance 'S '  then find out friction force acting on knife,

A particle moves in one dimension from rest under the influence of a force that varies with the distance travelled by the particle as shown in the figure. The kinetic energy (in Joule) of the particle after it has travelled 3 m is :

A uniform cable of mass ' $M^{\prime}$ and length $L^{\prime}$ is placed on a horizontal surface that its $\left[\frac{1}{n}\right]^{t h}$ part is hanging below the edge of the surface. To lift the hanging part of the cable up to the surface, the work done should be :

 Velocity-time graph for a body of mass 10 kg is shown in figure.  Work-done (in Joule) on the body in first two seconds of the motion is :

A particle of mass 100 g is thrown vertically upwards with a speed of 5 m/s. The work (in Joule) done by the force of gravity during the time the particle goes up is :

A mass of M kg is suspended by a weightless string . The horizontal force that is required to displace it until the string making an angle of 45^o  with the initial vertical direction is

A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement  x is proportional to :

A body of mass m starts moving from rest along the x-axis so that its velocity varies as
 where a is a constant and s is the distance covered by the body. The total
work done by all the forces acting on the body in the first t seconds after the start of
the motion is :

A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle, the motion of the particle takes place in a plane. It follows that : 

A body of mass 1kg falls freely from a height of 100m, on a platform of mass 3kg which is mounted on a spring having spring constant k = 1.25 X 10⁶N/m. The body sticks to the platform and the spring's maximum compression is found to be x. Given that g = 10ms^-2, the value of x (in cm) will be close to:

A block of mass m, lying on a smooth horizontal surface, is attached to a spring (of negligible mass), as shown in the figure. The block is initially at rest in its equilibrium position. If now the block is pulled with a constant force F, the maximum speed of the block is: 

A particle which is experiencing a force, given by undergoes a displacement of . If the particle had a kinetic energy of 3J at the beginning of the displacement, What is its kinetic energy (in Joule) at the end of the displacement?

A small block starts slipping down from a point $B$ on an inclined plane $A B$, which is making an angle $\theta$ with the horizontal. Section BC is smooth and the remaining section CA is rough with a coefficient of friction $\mu$. It is found that the block comes to rest as it reaches the bottom (point $A$ ) of the inclined plane. If BC = 2AC, the coefficient of friction is given by $\mu=k \tan \theta$. The value of k is $\qquad$ 

A cricket ball of mass is thrown vertically up, by a bowling machine, so that it rises to a maximum height of 20 m after leaving the machine. If the part pushing the ball applies a constant force on the ball and moves horizontally a distance of  while launching the ball the value of (is ). is

A block starts moving up an inclined plane of inclination $30^{\circ}$ with an initial velocity of $\nu_0$. It comes back to its initial $\frac{\nu_0}{2}$. position with velocity $\overline{2}$. The value of the coefficient of kinetic friction between the block and the inclined plane is close to $\frac{I}{1000}$, The nearest integer to $I$ is $\qquad$.

Two particles having masses 4 g and 16 g respectively are moving with equal kinetic energies. The ratio of the magnitudes of their
linear momentum is n: 2. The value of n will be ___________.

Two solids A and B of mass 1 kg and 2 kg respectively are moving with equal linear momentum. The ratio of their kinetic energies will be So the value of A will be ___________.

A boy is rolling a 0.5 kg ball on the frictionless floor with a speed of 20 ms ^-1 the ball gets deflected by an obstacle on the way. After deflection, it moves with 5% of its initial kinetic energy. What is the speed of the ball now?
 

A body of mass travels on straight line path with velocity . The net work done by the force during its displacement from is :

A bullet of mass 200 g having an initial kinetic energy of 90 J is shot inside a long swimming pool as shown in the figure. If its kinetic energy reduces to 40 J within 1 s, the minimum length of the pool, the bullet has to travel so that it completely comes to rest is

If the momentum of a body is increased by , then its kinetic energy increases by

If the Kinetic energy of a moving body becomes four times its initial Kinetic energy, then the percentage change in its momentum will be :

An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range

A bomb of mass  16 kg at rest explodes into two pieces of masses of 4  Kg and 12 Kg.  The velocity of the 12 Kg mass is 4 ms^{-1 .} The kinetic energy (in joule) of the other mass is :

A 2 kg block slides on a horizontal floor with a speed of 4 m/s. It strikes an uncompressed spring and compresses it till the block is motionless. The kinetic friction force is 15 N and the spring constant is 10,000 N/m. The spring compresses by (in cm) :

A body rolls down an inclined plane without slipping. The kinetic energy of rotation is of its translational kinetic energy. The body is :
 

Consider the following two statements:

(A) Linear momentum of a system of particles is zero

(B) The kinetic energy of a system of particles is zero

Then

What is the energy that an object possesses due to its motion called?

A block of mass 3.00 kg moving at a speed of 8.0 m/s accelerates at 6.00   for 7.00 s. Compute its final kinetic energy.

The total work done on a particle is equal to the change in its kinetic energy

A spherical body of mass 2 kg starting from rest acquires a kinetic energy of 10000 J at the end of 5th second. The force acted on the body is ______ N.

An object of mass ‘m’ initially at rest on a smooth horizontal plane starts moving under the action of force$F=2 \mathrm{~N}$. In the process of its linear motion, the angle $\theta$(as shown in figure) between the direction of force and horizontal varies as$\theta=\mathrm{kx}$, where k is constant and x is the distance covered by the object from the initial position. The expression of kinetic energy of the object will be$\mathrm{E}=\frac{\mathrm{n}}{\mathrm{k}} \sin \theta$. The value of n is ______.
                                      

A lift of mass is descending with the speed of . Its supporting cable begins to slip thus allowing it to fall with a constant acceleration of . The kinetic energy of the lift at the end of the fall through to a distance of will be _______

A particle of mass 10 g moves in a straight line with retardation 2x, where x is the displacement in SI units. Its loss of kinetic energy for above displacement is . The value of n will be ____________ .

A body is dropped on the ground from a height   and after hitting the ground, it rebounds to a height ''. If the ratio of velocities of the body just before and after hitting the ground is 4, then the percentage loss in kinetic energy of the body is   . The value of x is ________.

The momentum of a body is increased by 50%. The percentage increase in the kinetic energy of the body is_________ %.

Kept on a horizontal rough surface. The bullet gets embedded into the block and moves 20 m before coming to rest. The coefficient of friction between the block and the surface is _____.
 (Given $g=10 \mathrm{~m} / \mathrm{s}^2$ )

A body of mass is moving with a momentum of .Now a force of acts on the body in the direction of its motion for .The increase in the Kinetic energy of the body is________ J.

Given below are two statements :

Statements I: A truck and a car moving with the same kinetic energy are brought to rest by applying brakes which provide equal retarding forces. Both come to rest in equal distance.

Statements II: A car moving towards the east takes a turn and moves towards the north, the speed remains unchanged. The acceleration of the car is zero.

In the light of given statements, choose the most appropriate answer from the options given below

To maintain a speed of 80 km/h by a bus of mass 500 kg on a plane rough road for 4 km distance, the work done by the engine of the bus will be _______ KJ. [The coefficient of fiction between tyre of bus and road is 0.04. ]

Two bodies have kinetic energies in the ratio 16: 9. If they have the same linear momentum, the ratio of their masses respectively is:

A body of mass  kg is moving with a velocity of  m/s. Its kinetic energy will be

A car accelerates from rest to u m/s. The energy spent in this process is E J. The energy required to accelerate the car from u m/s to 2 u m/s is nE J. The value of n is ______.

A closed circular tube of average radius 15 cm , whose inner walls are rough, is kept in vertical plane. A block of mass 1 kg just fit inside the tube. The speed of block is $22 \mathrm{~m} / \mathrm{s}$, when it is introduced at the top of tube. After completing five oscillations, the block stops at the bottom region of tube. The magnitude of the work done by the tube on the block is
$\qquad$ J. (Given : $\left.g=10 \mathrm{~m} / \mathrm{s}^2\right)$
                                                             

A particle with a mass of 0.5 kg is moving in one dimension while it is subjected to a force that gives it a constant power of 0.9 W. If the particle's initial speed (measured in m/s) is zero, its speed (measured in m/s) 10-second is:

Two bodies of mass 4 g and 25 g are moving with equal kinetic energies. The ratio of the magnitude of their linear momentum is:

A proton is accelerated through 50,000 V. Its energy will increase by

If a rubber ball falls from a height of $h$ and rebounds up to the height of $ \frac{h}{2}$. The percentage loss of total energy of the initial system as well as the velocity ball before it strikes the ground, respectively, are :

A disc of mass m and radius r rolls on a horizontal plane without slipping with speed u. The total kinetic energy of the disc is

Ratio of average value of kinetic energy to that of potential energy for an SHM is.

As shown in Figure Two forces are acting on a block of mass m. Initially, block was at rest. If F₁ = 24N & h = 2m & K.E of block at position is 30J. Then what is the value of F₂  

A body of mass 2 kg is projected shown in figure what is its K.E at point P 

An object having mass $=2 \mathrm{~kg}$ experience a force $F=2 t^2 \hat{l}$ in x direction. Find work done by the force in first 3 sec .

If the % change in kinetic energy for a body is 25%. Then what is the % change in its momentum:

If $\% / 0$ change K.E for body is $25 \%$ then what is $\% / 0$ change in its momentum

A block is fastened to a horizontal spring. The block is pulled to a distance $x=10 \mathrm{~cm}$ from its equilibrium position (at $\mathrm{x}=0$ ) on a frictionless surface from rest. The energy of the block at $x=5 \mathrm{~cm} 0.25 \mathrm{~J}$. The spring constant of the spring is __________ $\mathrm{Nm}^{-1}$

A block moving horizontally on a smooth surface with a speed of $40 \mathrm{~ms}^{-1}$ splits into two equal parts. If one of the parts moves at $60 \mathrm{~ms}^{-1}$ in the same direction, then the fractional change in the kinetic energy will be $x: 4$ where $x=$
__________

A bullet of mass 50 g is fired with a speed of 100 m / s on a plywood and emerges with 40 m / s. The percentage loss of kinetic energy is :

A stone is projected at angle $30^{\circ}$ to the horizontal. The ratio of the kinetic energy of the stone at the point of projection to its kinetic energy at the highest point of flight will be -

A block of mass 10kg is moving in x-direction with a constant speed of 10 m/s . It is subjected to a retarding force F=-0.1 x joule / meter during its travel from x=20 meter to x=30 meter. Its final kinetic energy will be.
 

The graph between the resistive force F acting on a body and the distance covered by the body is shown in the figure. The mass of the body is 60 kg and the initial velocity is 3m/s. When the distance covered by the body is 4m, its kinetic energy will be

Four particles A, B, C, D of mass $\frac{\mathrm{m}}{2}$, m, 2m, 4m, have same momentum, respectively. The particle with maximum kinetic energy is :

A mass of 5 kg is moving along a circular path of radius 1 m. If the mass moves with 300 revolutions per minute, its kinetic energy would be
 

In the given figure, the block of mass m is dropped from the point 'A'. The expression for the kinetic energy of the block when it reaches point 'B' is

Direction : In the following question, a statement of Assertion $(A)$ is followed by a statement of reason (R). Mark the correct choice as :

Assertion : When the linear momentum of a body is doubled its kinetic energy becomes four-time
Reason : Kinetic energy of body $K E=\frac{P^2}{2 m}$

A block of mass 0.2 kg is attached to a spring of force-constant $4 \mathrm{~N} \mathrm{~m}^{-1}$. The coefficient of friction between the block and the floor is 0.05. Initially, the block is at rest and the spring is unstretched. An impulse is given to the block as shown in the figure. The block slides a distance of 0.08 m and comes to rest for the first time. Find out the initial velocity of the block in $\mathrm{ms}^{-1}$.

Three bodies A, B, and C have equal kinetic energies and their masses are 400 g, 1.2 kg and 1.6 kg respectively. The ratio of their linear momenta is :

When kinetic energy of a body becomes 36 times its original value, the percentage increase in the momentum of the body will be :

A small ball of mass m =2kg is connected to a fixed point O by an inextensible cord of length L = 2.4m The ball is resting on a smooth horizontal table at point A at a distance of 1 m from point O. It is imparted a horizontal velocity u in a direction perpendicular to the line OA. The string gets taut when the ball reaches point A'. What is the loss in kinetic energy as the strings get taut if the ball is initially given a velocity equal to the maximum allowable value?

(The maximum allowable value of u is when the impulse applied by the string on the support at O, reaches 3 N s.)

An electron and a proton are moving under the influence of mutual forces. In calculating the change in the kinetic energy of the system during motion, one ignores the magnetic force of one on another.
This is because,

A particle of charge Q, mass m is moving under the influence of a uniform electric field $
\text { Eî }
$ and a uniform magnetic field $
\text { Bk }
$ follows a trajectory from P to Q as shown in the figure. The velocities at P and Q are$v \hat{i}$ and $2 v \hat{j}$ respectively. Find the rate of work done by the electric field at P

A particle of mass $m$ moves on a straight line with its velocity increasing with distance according to the equation $\mathrm{v}=\alpha \sqrt{\mathrm{x}}$, where $\alpha$ is a constant. The total work done by all the forces applied on the particle during its displacement from $\mathrm{x}=0$ to $\mathrm{x}=\mathrm{d}$, will be:
 

A bead of mass ' $m$ ' slides without friction on the wall of a vertical circular hoop of radius ' $R$ ' as shown in the figure. The bead moves under the combined action of gravity and a massless spring (k) attached to the bottom of the hoop. The equilibrium length of the spring is ' $R$ '. If the bead is released from the top of the hoop with (negligible) zero initial speed, the velocity of the bead, when the length of the spring becomes ' $R$ ', would be (spring constant is ' k ', g is the acceleration due to gravity)

The power of car engine is 500 watt and mass of car is 1000 Kg . Then How much time would engine take to change its momentum from $25000 \frac{\mathrm{Km}}{\mathrm{sec}}$ to $4000 \frac{\mathrm{Km}}{\mathrm{sec}}$

A cord of negligible mass is wound around the rim of a wheel supported by spokes with negligible mass. The mass of wheel is 10 kg and radius is 10 cm and it can freely rotate without any friction. Initially the wheel is at rest. If a steady pull of 20 N is applied on the cord, the angular velocity of the wheel, after the cord is unwound by 1 m , would be :

A body of mass ' $m$ ' connected to a massless and unstretchable string goes in a vertical circle of radius ' R ' under gravity g. The other end of the string is fixed at the center of the circle. If the velocity at the top of the circular path is $ n\sqrt {\mathrm{gR}}$, where $\mathrm{n} \geq 1$, then the ratio of the kinetic energy of the body at the bottom to that at the top of the circle is