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An object having mass = 2kg  experience a forceF= 2t^{2}\widehat{i} in x - direction. Find work done by force in first 3 sec.

Given,  m = 2 kg

F  = 2t^2 i

a = F/m =  2t^2/2 = t^2 i

a = \frac{\mathrm{d} v}{\mathrm{d} t} = t^{2}

\int_{u}^{v} \mathrm{d} v = \int_{0}^{t}\mathrm{d}t^{2}dt

v - u = \frac{t^{3}}{3}

Assuming initial velocity was zero, u = 0

v = \frac{t^{3}}{3}

v = \frac{\mathrm{d} x}{\mathrm{d} t} = \frac{t^{3}}{3}

\Rightarrow \mathrm{d}x = \frac{t^{3}}{3}.\mathrm{d}t

We know that, dw = F.dx

\mathrm{d}W = 2t^{2}\times \frac{t^{3}}{3}.\mathrm{d}t

\int_{0}^{W}\mathrm{d}W =\int_{0}^{t} 2t^{2}\times \frac{t^{3}}{3}.\mathrm{d}t

W = \frac{t^{6}}{9} \; J

Put t = 3 secs

W = \frac{3^{6}}{9} \; J

W = 81 J

 

View Full Answer(1)
Posted by

Abhishek Sahu

 

4. 15.8m
 

Maximum height will be attained when the final velocity will become zero.

v^{2} -u^{2} = 2\left ( -g \right )h

0^{2} -15.3^{2} = 2\left ( -10 \right )h_{max}

h_{max } = 11.7 m

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Posted by

Abhishek Sahu

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A sonometer wire of length 1.5 m is made of steel. The tension in it produces an elastic strain of 1%. What is the fundamental frequency of steel if density and elasticity of steel are  7.7\times 10^{3}kg/m^{3}\; and\; 2.2\times 10^{11}N/m^{2} respectively ?

 

 

  • Option 1)

    770 Hz

  • Option 2)

    188.5 Hz

  • Option 3)

    178.2 Hz

  • Option 4)

    200.5 Hz

 

As we have learned

Young Modulus -

Ratio of normal stress to longitudnal strain

it denoted by Y

Y= \frac{Normal \: stress}{longitudnal\: strain}

- wherein

Y=\frac{F/A}{\Delta l/L}

F -  applied force

A -  Area

\Delta l -  Change in lenght

l - original length

 

 

 

 Fundamental frequency 

v = \frac{1}{2l }\cdot \sqrt{\frac{T}{\mu}}= \frac{1}{2l}\sqrt{\frac{T}{\rho A}}

\frac{1}{2l }\cdot \sqrt{\frac{stress}{\rho}}= \frac{1}{2\times 1.5}\sqrt{\frac{Y\times stress}{\rho }}

\frac{1}{3 }\cdot \sqrt{\frac{2.2 \times 10^1^1\times 10^{-2}}{7.7\times 10^3}} = 178.2 Hz

 

 

 

 

 

 


Option 1)

770 Hz

Option 2)

188.5 Hz

Option 3)

178.2 Hz

Option 4)

200.5 Hz

View Full Answer(1)
Posted by

SudhirSol

Which of the following is not based on the principle of capillarity

  • Option 1)

    Floating of wood on eater surface

  • Option 2)

    Ploughing of soil

  • Option 3)

    Rise of oil in wick of lantern

  • Option 4)

    Soaking of ink by bloating paper

 

As we discussed in concept

Capillary -

If a tube of very narrow bore is dipped in a liquid, the liquid in the capillary either ascends or descends .

- wherein

A towel soaks water.

 

Floating of wood on eater surface


Option 1)

Floating of wood on eater surface

Option is correct

Option 2)

Ploughing of soil

Option is incorrect

Option 3)

Rise of oil in wick of lantern

Option is incorrect

Option 4)

Soaking of ink by bloating paper

Option is incorrect

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Posted by

Aadil

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When the angle of contact between a solid and a liquid is 90°, then

  • Option 1)

    Cohesive force > Adhesive force

  • Option 2)

    Cohesive force < Adhesive force

  • Option 3)

    Cohesive force = Adhesive force

  • Option 4)

    Cohesive force >> Adhesive force

 

As we discussed in concept

Cause of viscosity -

Cause of viscosity  in liquids is cohesive

-

 

Cohesive force = Adhesive force


Option 1)

Cohesive force > Adhesive force

Option is incorrect

Option 2)

Cohesive force < Adhesive force

Option is incorrect

Option 3)

Cohesive force = Adhesive force

Option is correct

Option 4)

Cohesive force >> Adhesive force

Option is incorrect

View Full Answer(1)
Posted by

divya.saini

When impurities are added to an elastic substance, its elasticity

  • Option 1)

    Increases

  • Option 2)

    Decreases

  • Option 3)

    Becomes zero
     

  • Option 4)

    May increase or decrease

 

As we discussed in concept

Elasticity -

That body which regain it's original shape and size

- wherein

i.e. after removal of deforming force

 

both way increase or decrease


Option 1)

Increases

Option is incorrect

Option 2)

Decreases

Option is incorrect

Option 3)

Becomes zero
 

Option is incorrect

Option 4)

May increase or decrease

Option is correct

View Full Answer(1)
Posted by

prateek

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What is the change in surface energy, when a mercury drop of radius R splits up into 1000 droplets of radius r?

  • Option 1)

    8\rho R^{2}T

  • Option 2)

    16 \rho R^{2}T

  • Option 3)

    24 \rho R^{2}T

  • Option 4)

    36 \rho R^{2}T

 

As we discussed in concept

Surface Energy -

It is defined as the amount of work done in increasing the area of the liquid against surface tension.

-

 

  n\frac{4}{3}\pi r^{3}=\frac{4}{3}\pi R^{3}

nr^{3}=R^{3}

=> R=n^{1/3}r

where n= 10000

After calculeting we get r=36\rho R^2T


Option 1)

8\rho R^{2}T

Option is incorrect

Option 2)

16 \rho R^{2}T

Option is incorrect

Option 3)

24 \rho R^{2}T

Option is incorrect

Option 4)

36 \rho R^{2}T

Option is correct

View Full Answer(1)
Posted by

prateek

Water rises in a capillary tube to a certain height such that the upward force due to surface tension is balanced by 75 × 10-4 N, forces due to the weight of the liquid. If the surface tension of water is 6 × 10-2 N/m, the inner-circumference of the capillary must be

  • Option 1)

    1.25\times10^{-2}m

  • Option 2)

    0.50\times10^{-2}m

  • Option 3)

    6.5\times10^{-2}m

  • Option 4)

    12.5\times10^{-2}m
     

 

As we discussed in concept @14048 

Capillary -

If a tube of very narrow bore is dipped in a liquid, the liquid in the capillary either ascends or descends .

- wherein

A towel soaks water.

 

 Total upward force =circumference \times surface\: tension

 

=circumference\times 6\times 10^{-2}

Total upward force = weight of the liquid

=circumference\times 6\times 10^{-2}=75\times 10^{-4}

circumference =\frac{75\times 10^{-4}}{6\times 10^{-2}}

=12.5\times 10^{-2}m


Option 1)

1.25\times10^{-2}m

Option is incorrect

Option 2)

0.50\times10^{-2}m

Option is incorrect

Option 3)

6.5\times10^{-2}m

Option is correct

Option 4)

12.5\times10^{-2}m
 

Option is incorrect

View Full Answer(1)
Posted by

divya.saini

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There is no change in the volume of a wire due to change in its length on stretching. The poison’s ration of the material of the wire is

  • Option 1)

    + .50

  • Option 2)

    - 0.50

  • Option 3)

    0.25

  • Option 4)

    - 0.25
     

 

 

Strain -

Ratio of change in configuration to the original configuration.

-

 

 \sigma =-\frac{\frac{dr}{r}}{\frac{dl}{l}}

Volume of wire =\pi r^2l

r=\frac{D}{2}

v=\frac{\pi D ^2}{4}l

\frac{dv}{dl}=\frac{\pi }{4}2D dD +\pi D^2\times \frac{1}{4}dl

Volume remain constant

0=\frac{\pi l}{2D}dD+\frac{\pi D^2}{4d}

\sigma =\frac{dD.l}{D. dl}=\frac{2}{4}=0.5


Option 1)

+ .50

Incorrect

Option 2)

- 0.50

Correct

Option 3)

0.25

Incorrect

Option 4)

- 0.25
 

Incorrect

View Full Answer(1)
Posted by

Aadil

There is a hole in the bottom of tank having water. If total pressure at bottom is 3 atm (1 atm = 105N/m2) then the velocity of water flowing from hole is

  • Option 1)

    10 m/s

  • Option 2)

    30 m/s

  • Option 3)

    20 m/s

  • Option 4)

    none of these

 

As we discussed in

Torricelli's Theorem / Velocity of Efflux -

In fluid dynamics relating the speed of fluid flowing out of an orifice. 

- wherein

 

 Gauge pressure at bottom=2atm = 2\times 1.01\times 10^5 Pa

\rho gh=2\times 1.01\times 10^5^{}

10^3\times 10\times h=2\times 1.01\times 10^5

h= 2\times 10.1 =20.1

\therefore v_{eff}=\sqrt{2gh}=\sqrt{2\times 10\times 20.1}=20ms^{-1}


Option 1)

10 m/s

Incorrect

Option 2)

30 m/s

Incorrect

Option 3)

20 m/s

Correct

Option 4)

none of these

Incorrect

View Full Answer(1)
Posted by

Plabita

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