Gravitation · Physics · MHT CET

Earth is assumed to be a sphere of radius R. If '$$\mathrm{g}_\phi$$' is value of effective acceleration due to gravity at latitude $$30^{\circ}$$ and...

A body (mass $$\mathrm{m}$$ ) starts its motion from rest from a point distant $$R_0\left(R_0>R\right)$$ from the centre of the earth. The velocity ac...

Considering earth to be a sphere of radius '$$R$$' having uniform density '$$\rho$$', then value of acceleration due to gravity '$$g$$' in terms of $$...

The value of acceleration due to gravity at a depth '$$d$$' from the surface of earth and at an altitude '$$h$$' from the surface of earth are in the ...

If two planets have their radii in the ratio $$x: y$$ and densities in the ratio $$m: n$$, then the acceleration due to gravity on them are in the rat...

A mine is located at depth $$R / 3$$ below earth's surface. The acceleration due to gravity at that depth in mine is ($$R=$$ radius of earth, $$g=$$ a...

A body of mass '$$\mathrm{m}$$' is raised through a height above the earth's surface so that the increase in potential energy is $$\frac{\mathrm{mgR}}...

If two identical spherical bodies of same material and dimensions are kept in contact, the gravitational force between them is proportional to $$\math...

A body is projected vertically upwards from earth's surface of radius '$$R$$' with velocity equal to $$\frac{1^{\text {rd }}}{3}$$ of escape velocity....

A simple pendulum is oscillating with frequency '$$F$$' on the surface of the earth. It is taken to a depth $$\frac{\mathrm{R}}{3}$$ below the surface...

The depth at which acceleration due to gravity becomes $$\frac{\mathrm{g}}{2 \mathrm{n}}$$ is $$(\mathrm{R}=$$ radius of earth, $$\mathrm{g}=$$ accele...

Time period of simple pendulum on earth's surface is '$$\mathrm{T}$$'. Its time period becomes '$$\mathrm{xT}$$' when taken to a height $$\mathrm{R}$$...

The height at which the weight of the body becomes $$\left(\frac{1}{9}\right)^{\text {th }}$$ its weight on the surface of earth is $$(\mathrm{R}=$$ r...

Consider a light planet revolving around a massive star in a circular orbit of radius '$$r$$' with time period '$$T$$'. If the gravitational force of ...

The radius of the orbit of a geostationary satellite is (mean radius of earth is '$$R$$', angular velocity about own axis is '$$\omega$$' and accelera...

The ratio of energy required to raise a satellite to a height '$$h$$' above the earth's surface to that required to put it into the orbit at the same ...

The radius of earth is $$6400 \mathrm{~km}$$ and acceleration due to gravity $$\mathrm{g}=10 \mathrm{~ms}^{-2}$$. For the weight of body of mass $$5 \...

A body of mass '$$\mathrm{m}$$' kg starts falling from a distance 3R above earth's surface. When it reaches a distance '$$R$$' above the surface of th...

A body is projected vertically from earth's surface with velocity equal to half the escape velocity. The maximum height reached by the satellite is ( ...

A system consists of three particles each of mass '$$m_1$$' placed at the corners of an equilateral triangle of side '$$\frac{\mathrm{L}}{3}$$', A par...

A satellite moves in a stable circular orbit round the earth if (where $$\mathrm{V}_{\mathrm{H}}, \mathrm{V}_{\mathrm{c}}$$ and $$\mathrm{V}_{\mathrm{...

There is a second's pendulum on the surface of earth. It is taken to the surface of planet whose mass and radius are twice that of earth. The period o...

For a satellite orbiting around the earth in a circular orbit, the ratio of potential energy to kinetic energy at same height is

Periodic time of a satellite revolving above the earth's surface at a height equal to radius of the earth '$$R$$' is [ $$g=$$ acceleration due to grav...

Consider a planet whose density is same as that of the earth but whose radius is three times the radius '$$R$$' of the earth. The acceleration due to ...

A thin rod of length '$$L$$' is bent in the form of a circle. Its mass is '$$M$$'. What force will act on mass '$$m$$' placed at the centre of this ci...

A body weighs $$300 \mathrm{~N}$$ on the surface of the earth. How much will it weigh at a distance $$\frac{R}{2}$$ below the surface of earth? ( $$R ...

A seconds pendulum is placed in a space laboratory orbiting round the earth at a height '$$3 \mathrm{R}$$' from the earth's surface. The time period o...

A body weighs $$500 \mathrm{~N}$$ on the surface of the earth. At what distance below the surface of the earth it weighs $$250 \mathrm{~N}$$ ? (Radius...

The masses and radii of the moon and the earth are $$\mathrm{M_1, R_1}$$ and $$\mathrm{M_2, R_2}$$ respectively. Their centres are at a distance $$\ma...

The average density of the earth is [g is acceleration due to gravity]

The depth from the surface of the earth of radius $$\mathrm{R}$$, at which acceleration due to gravity will be $$60 \%$$ of the value on the earth sur...

Three point masses, each of mass 'm' are kept at the corners of an equilateral triangle of side 'L'. The system rotates about the centre of the triang...

The length of the seconds pendulum is lm on earth. If the mass and diameter of the planet is 1.5 times that of the earth, the length of the seconds pe...

If the horizontal velocity given to a satellite is greater than critical velocity but less than the escape velocity at the height, then the satellite ...

The period of revolution of planet $$\mathrm{A}$$ around the sun is 8 times that of planet $$\mathrm{B}$$. How many times the distance of A from the s...

The time period of a satellite of earth is 5 hours. If the separation between the earth and the satellite will satellite is increased to four times th...

A body of mass 'M' and radius 'R', situated on the surface of the earth becomes weightless at its equator when the rotational kinetic energy of the ea...

The mass of a spherical planet is 4 times the mass of the earth, but its radius (R) is same as that of the earth. How much work is done is lifting a b...

The radius of a planet is twice the radius of the earth. Both have almost equal average mass densities. If '$$V_P$$' and '$$V_E$$' are escape velociti...

Two satellites of same mass are launched in circular orbits at heights '$$R$$' and '$$2 R$$' above the surface of the earth. The ratio of their kineti...

At a height 'R' above the earth's surface the gravitational acceleration is (R = radius of earth, g = acceleration due to gravity on earth's surface)...

The mass of a planet is six times that of the earth. The radius of the planet is twice that of the earth. If the escape velocity from the earth is '$$...

For a body of mass '$$m$$', the acceleration due to gravity at a distance '$$R$$' from the surface of the earth is $$\left(\frac{g}{4}\right)$$. Its v...

The ratio of energy required to raise a satellite of mass '$$m$$' to height '$$h$$' above the earth's surface to that required to put it into the orbi...

A pendulum is oscillating with frequency '$$n$$' on the surface of the earth. It is taken to a depth $$\frac{R}{2}$$ below the surface of earth. New f...

When the value of acceleration due to gravity '$$g$$' becomes $$\frac{g}{3}$$ above surface of height '$$h$$' then relation between '$$h$$' and '$$R$$...

A particle of mass '$$m$$' is kept at rest at a height $$3 R$$ from the surface of earth, where '$$R$$' is radius of earth and '$$M$$' is the mass of ...

A body is projected from earth's surface with thrice the escape velocity from the surface of the earth. What will be its velocity when it will escape ...

The depth at which acceleration due to gravity becomes $$\frac{\mathrm{g}}{\mathrm{n}}$$ is [ $$\mathrm{R}$$ = radius of earth, $$\mathrm{g}=$$ accele...

The depth 'd' below the surface of the earth where the value of acceleration due to gravity becomes $$\left(\frac{1}{n}\right)$$ times the value at th...

The orbital velocity of an artificial satellite in a circular orbit just above the earth's surface is 'V'. For the satellite orbiting at an altitude o...

Earth has mass $M_1$ and radius $R_1$. Moon has mass $M_2$ and radius $R_2$. Distance between their centre is $r$. A body of mass $M$ is placed on the...

The escape velocity of a body from any planet, whose mass is six times the mass of earth and radius is twice the radius of earth will (v$_e$ = escape ...

The ratio of energy required to raise a satellite of mass $$m$$ to a height $$h$$ above the earth's surface of that required to put it into the orbit ...

As we go from the equator of the earth to pole of the earth, the value of acceleration due to gravity

The mass of earth is 81 times the mass of the moon and the distance between their centres is $$R$$. The distance from the centre of the earth, where g...

A body is thrown from the surface of the earth velocity $$\mathrm{v} / \mathrm{s}$$. The maximum height above the earth's surface upto which it will r...

Consider a particle of mass $m$ suspended by a string at the equator. Let $R$ and $M$ denote radius and mass of the earth. If $\omega$ is the angular ...

A hole is drilled half way to the centre of the earth. A body weighs 300 N on the surface of the earth. How much will, it weigh at the bottom of the h...

What is the minimum energy required to launch a satellite of mass ' $m$ ' from the surface of the earth of mass ' $M$ ' and radius ' $R$ ' at an altit...

The radius of the earth and the radius of orbit around the sun are 6371 km and $149 \times 10^6 \mathrm{~km}$ respectively. The order of magnitude of ...

 If $W_1, W_2$ and $W_3$ represent the work done in moving a particle from $A$ to $B$ along three different paths 1,2 and 3 (as shown in fig) in ...

The kinetic energy of a revolving satellite (mass $m$ ) at a height equal to thrice the radius of the earth $(R)$ is

A body is projected vertically from the surface of the earth of radius ' $R$ ' with velocity equal to half of the escape velocity. The maximum height ...