A man of mass m starts falling towards a planet of mass M and radius R. As he reaches near to the surface, he realizes that he will pass through a small hole in the planet. As he enters the hole, he sees that the planet is really made of two pieces a spherical shell of negligible thickness of mass 2M/3 and a point mass M/3 at the centre. Change in the force of gravity experienced by the man is

\(\frac{2}{3}\frac{GMm}{R^{2}}\)
\(\frac{1}{3}\frac{GMm}{R^{2}}\)
\(\frac{4}{3}\frac{GMm}{R^{2}}\)

Solution

A diametrical tunnel is dug across the Earth. A ball is dropped into the tunnel from one side. The velocity of the ball when it reaches the centre of the Earth is …. (Given :gravitational potential at the centre of Earth = –³⁄₂^GM⁄_R)

√R
\(\sqrt{gR}\)
\(\sqrt{2.5gR}\)
\(\sqrt{7.1gR}\)

Solution

A projectile is fired vertically from the Earth with a velocity kv_e where v_e is the escape velocity and k is a constant less than unity. The maximum height to which projectile rises,as measured from the centre of Earth, is

^R⁄_k
^R⁄_k-1
^R⁄_1-k²
^R⁄_1+k²

Solution

Suppose, the acceleration due to gravity at the Earth’s surface is 10 m s^-2 and at the surface of Mars it is 4.0 m s^-2. A 60 kg pasenger goes from the Earth to the Mars in a spaceship moving with a constant velocity. Neglect all other objects in the sky.Which part of figure best represents the weight (net gravitational force) of the passenger as a function of time?

Solution

g ∝ ¹⁄_R² so we will not get a straight line.

Also F = 0 at a point where Force due to Earth = Force due to mars

Explorer 38, a radio-astronomy satellite of mass 200 kg, circles the Earth in an orbit of average radius ^3R⁄₂ where R is the radius of the Earth. Assuming the gravitational pull on a mass of 1 kg at the earth’s surface to be 10 N,calculate the pull on the satellite

889 N
89 N
8889 N
8.9 N

Solution

The gravitational force of attraction between a uniform sphere of mass M and a uniform rod of length l and mass m oriented as shown is

\(\frac{GMm}{r(r+\iota )}\)
\(\frac{GMm}{r^{2}}\)
Mmr²+l
(r²+l)mM

Solution

If there were a small gravitational effect, then which of the following forces will undergo a change?

Viscous force
Electrostatic force
Magnetic force
Archimedes' uplift

Solution

Weight of liquid displaced = mg.

Two identical geostationary satellites are moving with equal speeds in the same orbit but their sense of rotation brings them on a collision course. The debris will

fall down
move up
begin to move from east to west in the same orbit
begin to move from west to east in the same orbit

Solution

The total momentum will be zero and hence velocity will be zero just after collisiion. The pull of earth will make it fall down.

If ear this supposed to be a sphere of radius R, if g₃₀ is value of acceleration due to gravity at lattitude of 30° and g at the equator, the value of g – g₃₀ is

¹⁄₄ω²R
³⁄₄ω²R
ω²R
¹⁄₂ω²R

Solution

A ball is dropped from a satellite revolving around the ear that height of 120 km. The ball will

continue to move with same speed along a straight line tangentially to the satellite at that time
continue to move with same speed along the original orbit of satellite.
fall down to earth gradually
go far away in space

Solution

The orbital speed of satellite is independent of mass of satellite,so ball will behave as a satellite & will continue to move with same speed in original orbit.

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