Engineering

8 Views |

**Question**

Asked in: BITSAT-2018

From a sphere of mass M and radius R, a smaller sphere of radius is carved out such that the cavity made in the original sphere is between its centre and the periphery. (See figure). For the configuration in the figure where the distance between the centre of the original sphere and the removed sphere is 3R, the gravitational force between the two spheres is :

**Question**

Asked in: BITSAT-2018

From a sphere of mass M and radius R, a smaller sphere of radius is carved out such that the cavity made in the original sphere is between its centre and the periphery. (See figure). For the configuration in the figure where the distance between the centre of the original sphere and the removed sphere is 3R, the gravitational force between the two spheres is :

Solution : Volume of removed sphere, Volume of the sphere (remaining)
Therefore mass of sphere carved and remaining sphere are at respectively
1/8M and 7/8M.Therefore, gravitational force between these two sphere,

Engineering

204 Views |

When body is raised to a height equal to radius of earth, the P.E. change is

- Option 1)
- Option 2)
- Option 3)
- Option 4)
none of these

As we learnt in
Gravitational Potential energy at a point -
gravitational potential energy
Mass of source body
mass of test body
distance between two
- wherein
Always negative in the gravitational field because Force is attractive in nature.
Potential energy =
at surface of earth
when it is raised at h-R,
Option 1)
This is incorrect option
Option 2)
This is correct...

Engineering

797 Views |

What would be the duration of the year if the distance between the earth and the sun gets doubled?

- Option 1)
1032 days

- Option 2)
129 days

- Option 3)
365 days

- Option 4)
730 days

As we learnt in

Kepler's 3rd law -

From fig.

semi major Axis

Perigee

- wherein

Known as law of periods

apogee

If r get double

**Option 1)**

**1032 days**

**This is correct option**

Option 2)

129 days

This is incorrect option

Option 3)

365 days

This is incorrect option

Option 4)

730 days

This is incorrect option

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Engineering

593 Views |

Two planets of radii r1 and r2 are made from the same material. The ratio of the acceleration due to gravity g1/g2 at the surface of the two planets is

- Option 1)
- Option 2)
- Option 3)
- Option 4)

As we learnt in
Acceleration due to gravity (g) -
Force extended by earth on a body is gravity.
Formula:
gravity
density of earth
Radius of earth
- wherein
It's average value is on the surface of earth
Since both are made of same material hence their densities are equal
Option 1)
This is correct option
Option 2)
This is incorrect option
Option 3)
This is incorrect...

Engineering

120 Views |

The radii of the earth and the moon are in the ratio 10 : 1 while acceleration due to gravity on the earth’s surface and moon’s surface are in the ratio 6 : 1. The ratio of escape velocities from earth’s surface to that of moon surface is

- Option 1)
- Option 2)
6 : 1

- Option 3)
1.66 : 1

- Option 4)
7.74 : 1

As we learnt in
Acceleration due to gravity (g) -
Force extended by earth on a body is gravity.
Formula:
gravity
density of earth
Radius of earth
- wherein
It's average value is on the surface of earth
Escape velocity =
Option 1)
This is incorrect option
Option 2)
6 : 1
This is incorrect option
Option 3)
1.66 : 1
This is incorrect option
Option 4)
7.74 : 1
This is correct option

Engineering

545 Views |

The masses of two planets are in the ratio 1 : 2. Their radii are in the ratio 1 : 2. The acceleration due to gravity on the planets are in the ratio.

- Option 1)
1 : 2

- Option 2)
2 : 1

- Option 3)
3 : 5

- Option 4)
5 : 3

As we learnt in
Acceleration due to gravity (g) -
Force extended by earth on a body is gravity.
Formula:
gravity
density of earth
Radius of earth
- wherein
It's average value is on the surface of earth
Option 1)
1 : 2
This is correct option
Option 2)
2 : 1
This is incorrect option
Option 3)
3 : 5
This is incorrect option
Option 4)
5 : 3
This is incorrect option

Engineering

1321 Views |

The largest and the shortest distance of the earth from are r1 and r2. It’s distance from the sun when it is perpendicular to the major-axis of the orbit drawn from the sun.

- Option 1)
- Option 2)
- Option 3)
- Option 4)

As we learnt in
Velocity of planet in terms of Eccentricity -
Velocity of planet at apogee
- wherein
Eccentricity (e) =
The position of a particle moving in an elliptical orbit is represented as
is perpendicular distance of particle from focus and e is eccentricity of ellipse
Option 1)
This is incorrect option
Option 2)
This is incorrect option
Option 3)
This is correct...

Engineering

343 Views |

The figure shows the motion of a planet around the sun in an elliptical orbit with sun at the focus. The shaded areas A and B are also shown in the figure which can be assumed to be equal. If t1 and t2 represent the time for the planet to move from a to b and d to c respectively, then

- Option 1)
t1 > t2

- Option 2)
t1 < t2

- Option 3)
t1 = t2

- Option 4)
none of these

As we learnt in
Kepler's 2nd law -
Area of velocity =
Areal velocity
small area traced
- wherein
Simiar to Law of conservation of momentum
Angular momentum
Known as Law of Area
Areal velocity of planet in elliptical path is constant. This implies equal area will be covered in equal time.
Option 1)
t1 > t2
This is incorrect option
Option 2)
t1 < t2
This is incorrect option
Option...

Engineering

106 Views |

The escape velocity from the earth’s surface is 11 km/sec. A certain planet has a radius twice that of the earth but its mean density is the same as that of the earth. The value of the escape velocity from this planet would be

- Option 1)
22 km/sec

- Option 2)
11 km/sec

- Option 3)
5.5 km/sec

- Option 4)
16.5 km/sec

As we learnt in
Escape velocity ( in terms of radius of planet) -
Escape velocity
Radius of earth
- wherein
depends on the reference body
greater the value of or greater will be the escape velocity For earth
Option 1)
22 km/sec
This is correct option
Option 2)
11 km/sec
This is incorrect option
Option 3)
5.5 km/sec
This is incorrect option
Option 4)
16.5 km/sec
This is...

Engineering

295 Views |

The escape velocity from earth is 11.2 km per sec. If a body is to be projected in a direction making an angle 45° to the vertical, then the escape velocity is

- Option 1)
11.2 × 2 km/sec

- Option 2)
11.2 km/sec

- Option 3)
Km/sec

- Option 4)

As we learnt in
Escape velocity -
Minimum velocity which is required to escape the body from earth's gravitational pull
- wherein
It is independent of the mass and direction of projection of body.
Escape velocity is independent of direction of projection. Hence it will remain same for all direction.
Option 1)
11.2 × 2 km/sec
This is incorrect option
Option 2)
11.2 km/sec
This is correct...

Engineering

142 Views |

The distance of two planets from sun are nearly 10^{14} and 10^{12} meters. Assuming that they move in circular orbits, their periodic times will be in the ratio

- Option 1)
100

- Option 2)
10

- Option 3)
1000

- Option 4)

As we learnt in
Kepler's 3rd law -
From fig.
semi major Axis
Perigee
- wherein
Known as law of periods
apogee
or
Option 1)
100
This is incorrect option
Option 2)
10
This is incorrect option
Option 3)
1000
This is correct option
Option 4)
This is incorrect option

Engineering

486 Views |

The distance between centre of the earth and moon is 384000 km. If the mass of the earth is 6 × 10^{24} kg and G = 6.66 × 10^{–11} Nm^{2}/kg^{2}. The speed of the moon is nearly

- Option 1)
1 km/sec

- Option 2)
4 km/sec

- Option 3)
8 km/sec

- Option 4)
11.2 km/sec

As we learnt in
Orbital velocity of satellite -
Position of satellite from the centre of earth
Orbital velocity
- wherein
The velocity required to put the satellite into its orbit around the earth.
Option 1)
1 km/sec
This is correct option
Option 2)
4 km/sec
This is incorrect option
Option 3)
8 km/sec
This is incorrect option
Option 4)
11.2 km/sec
This is incorrect option

Engineering

121 Views |

If the radius of the earth were to shrink by one percent, its mass remaining the same, the acceleration due to gravity on the earth’s surface would

- Option 1)
decrease

- Option 2)
remains unchanged

- Option 3)
increase

- Option 4)
none of these

As we learnt in
Percentage decrease in value of 'g' -
Variation in 'g'
Radius
- wherein
rate of decrease of gravity outside the earth (h<<R) is double of that of inside the earth.
If
g will increase by 2% .
Option 1)
decrease
This is incorrect option
Option 2)
remains unchanged
This is incorrect option
Option 3)
increase
This is correct option
Option 4)
none of these
This is...

Engineering

401 Views |

If the radius of earth's orbit is made 1/16, the duration of an year will become

- Option 1)
16 times

- Option 2)
1/64 times

- Option 3)
1/16 times

- Option 4)
1/8 times

As we learnt in
Kepler's 3rd law -
From figure
semi major Axis
Perigee
- wherein
Known as law of periods
apogee
Option 1)
16 times
This is incorrect option
Option 2)
1/64 times
This is correct option
Option 3)
1/16 times
This is incorrect option
Option 4)
1/8 times
This is incorrect option

Engineering

117 Views |

If the acceleration due to gravity of a planet is half the acceleration due to gravity of earth’s surface and radius of planet is half the radius of the earth, the mass of planet in terms of mass of earth is

- Option 1)
- Option 2)
- Option 3)
- Option 4)

As we learnt in
Acceleration due to gravity (g) -
Force extended by earth on a body is gravity.
Formula:
gravity
density of earth
Radius of earth
- wherein
It's average value is on the surface of earth
and
Option 1)
This is incorrect option
Option 2)
This is incorrect option
Option 3)
This is incorrect option
Option 4)
This is correct option

Engineering

138 Views |

If g is the acceleration due to gravity of the earth’s surface the gain in the potential energy of an object of mass m raised from the surface of the earth to a height equal to the radius R of the earth is

- Option 1)
- Option 2)
- Option 3)
- Option 4)

As we learnt in
Gravitational Potential energy at a point -
gravitational potential energy
Mass of source body
mass of test body
distance between two
- wherein
Always negative in the gravitational field because Force is attractive in nature.
Potential energy at earth's surface
Potential energy at height
gain in potential energy
Option 1)
This is correct option
Option...

Engineering

149 Views |

If escape velocity from the earth’s surface is 11.2 km/sec. then escape velocity from a planet of mass same as that of earth but radius one fourth as that of earth is

- Option 1)
11.2 km/sec

- Option 2)
22.4 km/sec

- Option 3)
5.65 km/sec

- Option 4)
44.8 km/sec

As we learnt in
Escape velocity ( in terms of radius of planet) -
Escape velocity
Radius of earth
- wherein
depends on the reference body
greater the value of or greater will be the escape velocity For earth
Escape velocity
Option 1)
11.2 km/sec
This is incorrect option
Option 2)
22.4 km/sec
This is correct option
Option 3)
5.65 km/sec
This is incorrect option
Option 4)
44.8...

Engineering

283 Views |

An earth’s satellite of mass m revolves in a circular orbit at a height h from the surface g is acceleration due to gravity at the surface of the earth. The velocity of the satellite in the orbit is given by

- Option 1)
- Option 2)
- Option 3)
- Option 4)

As we learnt in
Variation in 'g' with height -
gravity at height from surface of earth.
Radius of earth
height above surface
- wherein
At height h, effect of gravity is
Option 1)
This is incorrect option
Option 2)
This is incorrect option
Option 3)
This is incorrect option
Option 4)
This is correct option

Engineering

362 Views |

A spherical planet far out in space has a mass M_{0} and diameter D_{0}. A particle of mass m falling freely near the surface of this planet will experience an acceleration due to gravity which is equal to

- Option 1)
- Option 2)
- Option 3)
- Option 4)

As we learnt in
Acceleration due to gravity (g) -
Force extended by earth on a body is gravity.
Formula:
gravity
density of earth
Radius of earth
- wherein
It's average value is on the surface of earth
Acceleration due to gravity
Option 1)
This is incorrect option
Option 2)
This is incorrect option
Option 3)
This is correct option
Option 4)
This is incorrect option

Engineering

692 Views |

A satellite of mass m is circulating around the earth with constant angular velocity. If radius of the orbit is R_{0} and mass of the earth M, the angular momentum about the centre of the earth is

- Option 1)
- Option 2)
- Option 3)
- Option 4)

As we learnt in
Angular momentum of satellite -
Angular momentum
mass of satellite
- wherein
depends on both the masses , mass of centre of body and mass of planet as well as radius of earth.
Centripetal force =
Angular momentum =
Option 1)
This is incorrect option
Option 2)
This is incorrect option
Option 3)
This is incorrect option
Option 4)
This is correct option

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