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Q.1. Calculate the change in the value of g at altitude 45°. Take radius of earth = 6.37 × 10^{3} km
Sol.
= g 0.0168 m/s^{2}
Dg = gg' = 0.0168 m/s^{2 }
Q.2. Determine the speed with which the earth would have to rotate on its axis, so that a person on the equator would weigh 3/5th as much as at present. Take R = 6400 km
Sol.
Q.3. At what height from the surface of earth will the value of g be reduced by 36% from the value at the surface? R = 6400 km
Sol.
Q.4. The distance between two bodies A and B is r. Taking the gravitational force according to the law of inverse square of r, the acceleration of the body A is a. If the gravitational force follows an inverse fourth power law, then what will be the acceleration of body A?
Sol.
Q.5. Find the force of attraction on a particle of mass m placed at the centre of a semicircular wire of length L and mass M.
Sol.
Q.1. A particle of mass m is placed at the centre of a uniform spherical shell of same mass and radius R. Find the gravitational potential at a distance R/2 from the centre.
Sol.
V = V_{e }+ V_{s} =
Q.2. A particle of mass 20 g experiences a gravitational force of 4.0 N along positive xdirection. Find the gravitational field at that point.
Sol.
200 N/kg i
Q.3. The gravitational potential due to a mass distribution is V = 3x^{2}y + y^{3}z. Find the gravitational field.
Sol.
Q.4. Gravitational potential at x = 2 m is decreasing at a rate of 10 J/kgm along the positive xdirection. It implies that the magnitude of gravitational field at x = 2 m is also 10 N/kg. Is this statement true or false?
Sol. Only the variation is given along xaxis, nothing is about y and z axis, so, the statement is false.
Q.5. The gravitational potential in a region is given by, V = 20(x+ y) J/kg. Find the magnitude of the gravitational force on a particle of mass 0.5 kg placed at the origin.
Sol.
Q.6. The gravitational field in a region is given by
Find the work done by the gravitational field when a particle of mass 1 kg is moved on the line 3y + 2x = 5 from (1 m, 1 m) to (2 m, 3 m).
Sol.
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127 videos464 docs210 tests
