If value of acceleration due to gravity changes from one place to another, which of the following forces will undergoa change ?

Viscous force
Buoyant force
Magnetic force
All of the above

Solution

As buoyant force involves ‘g’ in it.

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

–E₀
1.5 E₀
2E₀
E₀

The radii of two planets are respectively R₁ and R₂ and their densities are respectively ρ₁ and ρ₂. The ratio of the accelerations due to gravity at their surfaces is

\(g_{1}:g_{2}=\frac{\rho _{1}}{R_{1}^{2}}:\frac{\rho _{2}}{R_{2}^{2}}\)
g₁:g₂ = R₁R₂:ρ₁ρ₂
g₁:g₂ = R₁ρ₂:R₂ρ₁
g₁:g₂ = R₁ρ₁:R₂ρ₂

Solution

g ∝ ρR

The ratio of the kinetic energy required to be given to a satellite so that it escapes the gravitational field of Earth to the kinetic energy required to put the satellite in a circular orbit just above the free surface of Earth is

Solution

The gravitational potential difference between the surface of a planet and a point 20 m above the surface is 2 joule/kg.If the gravitational field is uniform, then the work done in carrying a 5 kg body to a height of 4 m above the surface is

2 J
20 J
40 J
10 J

Solution

For uniform gravitational field

E_g = - ^v⁄_r = -^-2⁄₂₀ = ¹⁄₁₀ ms^-2

Now,W = mgh = 5 × ¹⁄₁₀ × 4 = 2J

A uniform ring of mass m and radius r is placed directly above a uniform sphere of mass M and of equal radius. The centre of the ring is directly above the centre of the sphere at a distance r√3 as shown in the figure.The gravitational force exerted by the sphere on the ring will be

\(\frac{GMm}{8r^{2}}\)
\(\frac{GMm}{4r^{2}}\)
\(\sqrt{3}\frac{GMm}{8r^{2}}\)
\(\frac{GMm}{8r^{3}\sqrt{3}}\)

Solution

There are _______ gravitational lines of force inside a spherically symmetric shell.

infinitely many
zero
varying number depending upon surface area
varying number depending upon volume

Solution

There is no gravitational field in the shell.

Consider Earth to be a homogeneous sphere. Scientist A goes deep down in a mine and scientist B goes high up in a balloon. The gravitational field measured by

A goes on decreasing and that by B goes on increasing
B goes on decreasing and that by A goes on increasing
each decreases at the same rate
each decreases at different rates

Solution

Both decreases but variation are different.

Mass of the Earth has been determined through

use of Kepler's ^T²⁄_R³ constancy law and Moon's period
sampling the density of Earth's crust and using Earth's radius
Cavendish's determination of G and using Earth radius and g at its surface
use of periods of satellites at different heights above Earth's surface and known radius of Earth

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

g R²/(R + h)
g R
gR/(R –h)
\(\sqrt{[gR^{2}/(R+h)]}\)

Solution

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