RamanFlame Institute

A sphere of mass M and radius

A sphere of mass M and radius R2 has a concentric cavity of radius R1 as shown in figure. The force F exerted by the sphere on a particle of mass m located at a distance r from the centre …

The diagram showing the variation of gravitational potential of earth with distance from the centre of earth is

Answer: c (14)

Assuming the earth to have a constant density, point out which of the following curves show the variation of acceleration due to gravity from the centre of earth to the points far away from the surface of earth

Answer: c (6)

A geostationary satellite orbits around the earth in a circular orbit of radius

A geostationary satellite orbits around the earth in a circular orbit of radius 36000 km. Then, the time period of a satellite orbiting a few hundred kilometres above the earth’s surface (REarth = 6400 km ) will approximately be (a) 1/2 …

If the distance between the earth and the sun becomes half its present value, the number of days in a year would have been

(a) 64.5 (b) 129 (c) 182.5 (d) 730 Answer: b (23)

A satellite is launched into a circular orbit of radius R around the earth. A second satellite is launched into an orbit of radius (1.01)R. The period of the second satellite is larger than that of the first one by approximately

(a) 0.5% (b) 1.0% (c) 1.5% (d) 3.0% Answer: c (8)

A projectile is projected with velocity

A projectile is projected with velocity kve in vertically upward direction from the ground into the space. (ve is escape velocity and k<1) . If air resistance is considered to be negligible then the maximum height from the centre of …

Two bodies of masses m1 and m2 are initially at rest at infinite distance apart. They are then allowed to move towards each other under mutual gravitational attraction. Their relative velocity of approach at a separation distance r between them is

Two bodies of masses m1 and m2 are initially at rest at infinite distance apart. They are then allowed to move towards each other under mutual gravitational attraction. Their relative velocity of approach at a separation distance r between them …

A solid sphere of uniform density and radius 4 units is located with its centre at the origin O of coordinates. Two spheres of equal radii 1 unit with their centres at A(– 2, 0, 0) and B(2, 0, 0) respectively are taken out of the solid leaving behind spherical cavities as shown in figure

(a) The gravitational force due to this object at the origin is zero (b) The gravitational force at the point B (2, 0, 0) is zero (c) The gravitational potential is the same at all points of the circle y2+ …

A rocket of mass M is launched vertically from the surface of the earth with an initial speed V. Assuming the radius of the earth to be R and negligible air resistance, the maximum height attained by the rocket above the surface of the earth is

Answer: c (7)

A body of mass m is taken from earth surface to the height h equal to radius of earth, the increase in potential energy will be

(a) mgR (b) 1/2 mgR (c) 2 mgR (d) 1/4 mgR Answer: b (251)

An artificial satellite moving in a circular orbit around the earth has a total (kinetic + potential) energy

An artificial satellite moving in a circular orbit around the earth has a total (kinetic + potential) energy E0. Its potential energy is (a) – E0 …

A simple pendulum has a time period

A simple pendulum has a time period T1 when on the earth’s surface and T2 when taken to a height R above the earth’s surface, where R is the radius of the earth. The value of T2/T1 is (a) 1 …

The radius and mass of earth are increased by 0.5%. Which of the following statements are true at the surface of the earth

(a) g will increase (b) g will decrease (c) Escape velocity will remain unchanged (d) Potential energy will remain unchanged Answer: Answer: (b,c,d) (9)

In order to make the effective acceleration due to gravity equal to zero at the equator, the angular velocity of rotation of the earth about its axis should be

In order to make the effective acceleration due to gravity equal to zero at the equator, the angular velocity of rotation of the earth about its axis should be (g= 10 ms-2 and radius of earth is 6400 kms) (a) …

If the radius of the earth were to shrink by 1% its mass remaining the same, the acceleration due to gravity on the earth’s surface would

(a) Decrease by 2% (b) Remain unchanged (c) Increase by 2% (d) Increase by 1% Answer: c (5)

Suppose the gravitational force varies inversely as the

Suppose the gravitational force varies inversely as the nth power of distance. Then the time period of a planet in circular orbit of radius R around the sun will be proportional to (a) R(n+1/2) …

A mass M is split into two parts, m and (M–m), which are then separated by a certain distance. What ratio of m/M maximizes the gravitational force between the two parts

(a) 1/3 (b) 1/2 (c) 1/4 (d) 1/5 Answer: b (6)

A satellite S is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of earth

(a) The acceleration of S is always directed towards the centre of the earth (b) The angular momentum of S about the centre of the earth changes in direction but its magnitude remains constant (c) The total mechanical energy of …

The magnitudes of the gravitational force at distances r1 and r2 from the centre of a uniform sphere of radius R and mass M are F1 and F2 respectively. Then Answer: A (12)

Imagine a light planet revolving around a very massive star in a circular orbit of radius R with a period of revolution T. If the gravitational force of attraction between planet and star is proportional R-(5/2)to , then T2 is proportional …

Earth is revolving around the sun if the distance of the Earth from the Sun is reduced to 1/4th of the present distance then the present day length reduced by

(a) 1/4 (b) 1/2 (c) 1/8 …

The condition for a uniform spherical mass m of radius r to be a black hole is [G= gravitational constant and g= acceleration due to gravity]

(a) (2Gm/r)1/2≤c (b) (2Gm/r)1/2=c (c) (2Gm/r)1/2≥c (d) (gm/r)1/2≥c Answer: c (4)

Two satellite are revolving around the earth with velocities

Two satellite are revolving around the earth with velocities v1 and v2 and in radii r1 and r2 (r1 > r2) respectively Then (a) v1 = v2 …

Hubble’s law states that the velocity with which milky way is moving away from the earth is proportional to

(a) Square of the distance of the milky way from the earth (b) Distance of milky way from the earth (c) Mass of the milky way (d) Product of the mass of the milky way and its distance from the …

If orbital velocity of planet is given by

If orbital velocity of planet is given by v =Ga Mb Rc , then (a) a=1/3,b=1/3,c=-1/3 (b) a=1/2,b=1/2,c=-1/2 (c) a=1/2,b=-1/2,c=-1/2 (d) a=1/2,b=-1/2,c=-1/2 Answer: b (8)

The mass of a planet that has a moon whose time period and orbital radius are T and R respectively can be written as

(a) 4π2 R3 G-1T-2 (b) 8π2 R3 G-1T-2 (c) 12π2 R3 G-1T-2 (d) 16π2 R3 G-1T-2 Answer: a (10)

The eccentricity of earth’s orbit is 0.0167. The ratio of its maximum speed in its orbit to its minimum speed is

(a) 2.507 (b) 1.033 (c) 8.324 (d) 1.000 Answer: b (7)

The period of moon’s rotation around the earth is nearly 29 days. If moon’s mass were 2 fold, its present value and all other things remained unchanged, the period of moon’s rotation would be nearly

(a) 29√2 days (b) 29 /√2 days (c) 29 × 2 days (d) 29 days Answer: d (4)

A body revolved around the sun 27 times faster then the earth what is the ratio of their radii

(a) 1/3 (b) 1/9 (c) 1/27 (d) 1/4 Answer; b (3)

The maximum and minimum distances of a comet from the sun are

The maximum and minimum distances of a comet from the sun are 8 × 1012 m and 1.6 × 1012 m . If its velocity when nearest to the sun is 60 m/s, what will be its velocity in m/s …

In the solar system, which is conserved

(a) Total Energy (b) K.E. (c) Angular Velocity (d) Linear Momentum Answer: a (10)

What does not change in the field of central force

(a) Potential energy (b) Kinetic energ (c) Linear momentum (d) Angular momentum Answer:D (10)

Suppose the law of gravitational attraction suddenly changes and becomes an inverse cube law i.e F∞1/r3 . , but still remaining a central force. Then

(a) Keplers law of areas still holds (b) Keplers law of period still holds (c) Keplers law of areas and period still hold (d) Neither the law of areas, nor the law of period still holds Answer: d (14)