The acceleration of the moon just before it strikes the earth in the previous question is:
- 10ms-2
- 0.0027ms-2
- 6.4ms-2
- 5.0ms-2
Question types
Gravitation question types
81 questions across 5 question groups — pick any mix to generate a Physics paper with step-by-step answer keys.
81
Questions
5
Question groups
5
Question types
01
M.C.Q (1 Marks)
23 Q→022 Marks Questions
23 Q→033 Marks Question
19 Q→044 Marks Question
2 Q→055 Marks Questions
14 Q→Sample Questions
Gravitation questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
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A particle is kept at rest at a distance R (earth's radius) above the earth's surface. The minimum speed with which it should be projected so that it does not return is:
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$\sqrt{\frac{\text{GM}}{4\text{R}}}$
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$\sqrt{\frac{\text{RM}}{2\text{R}}}$
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$\sqrt{\frac{\text{GM}}{\text{R}}}$
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$\sqrt{\frac{2\text{GM}}{\text{R}}}$
The kinetic energy needed to project a body of mass m from the earth's surface to infinity is:
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$\frac{1}{4}\text{mgR}$
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$\frac{1}{2}\text{mgR}$
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$\text{mgR}$
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$2\text{mgR}$
Let V and E represent the gravitational potential and field at a distance r from the centre of a uniform solid sphere. Consider the two statements:
- The plot of V against r is discontinuous.
- The plot of E against r is discontinuous.
- Both A and B are correct.
- A is correct but B is wrong.
- B is correct but A is wrong.
- Both A and B are wrong.
Inside a uniform spherical shell:
- The gravitational potential is zero.
- The gravitational field is zero.
- The gravitational potential is same everywhere.
- The gravitational field is same everywhere.
Two concentric spherical shells have masses M1, M2 and radii R1, R2 (R1, < R2). What is the force exerted by this system on a particle of mass m1 if it is placed at a distance $\frac{\text{R}_1+\text{R}_2}{2}$ from the centre?
View full solution →Find the acceleration due to gravity in a mine of depth 640m if the value at the surface is 9.800m/s2. The radius of the earth is 6400km.
A mass of 6 × 1024kg (equal to the mass of the earth) is to be compressed in a sphere in such a way that the escape velocity from its surface is 3 × 108m/s. What should be the radius of the sphere?
Three particles of mass m each are placed at the three corners of an equilateral triangle of side a. Find the work which should be done on this system to increase the sides of the triangle to 2a.
At what rate should the earth rotate so that the apparent g at the equator becomes zero? What will be the length of the day in this situation?
A pendulum having a bob of mass m is hanging in a ship sailing along the equator from east to west. When the ship is stationary with respect to water the tension in the string is T0.
View full solution →- Find the speed of the ship due to rotation of the earth about its axis.
- Find the difference between T0 and the earth's attraction on the bob.
- If the ship sails at speed v, what is the tension in the string? Angular speed of earth's rotation is $\omega$ and radius of the earth is R.
The gravitational potential energy of a two particle system is derived in this chapter as $\text{U}=-\frac{\text{Gm}_1\text{m}_2}{\text{r}}.$ Does it follow from this equation that the potential energy for $\text{r}=\infty$ must be zero? Can we choose the potential energy for $\text{r}=\infty.$ to be 20J and still use this formula? If no, what formula should be used to calculate the gravitational potential energy at separation r?
View full solution →A tunnel is dug along a chord of the earth at a perpendicular distance $\frac{\text{R}}{2}$ from the earth's centre. The wall of the tunnel may be assumed to be frictionless. Find the force exerted by the wall on a particle of mass m when it is at a distance x from the centre of the tunnel.
View full solution →If heavier bodies are attracted more strongly by the earth, why don't they fall faster than the lighter bodies?
The time taken by Mars to revolve round the sun is 1.88 years. Find the ratio of average distance between Mars and the sun to that between the earth and the sun.
No part of India is situated on the equator. Is it possible to have a geostationary satellite which always remains over New Delhi?
Find the acceleration due to gravity of the moon at a point 1000km above the moon's surface. The mass of the moon is 7.4 × 1022kg and its radius is 1740km.
- Find the radius of the circular orbit of a satellite moving with an angular speed equal to the angular speed of earth's rotation.
- If the satellite is directly above the north pole at some instant, find the time it takes to come over the equatorial plane. Mass of the earth = 6 × 1024kg.
A satellite of mass 1000kg is supposed to orbit the earth at a height of 2000km above the earth's surface. Find
- Its speed in the orbit.
- Its kinetic energy.
- The potential energy of the earth-satellite system.
- Its time period. Mass of the earth = 6 × 1024kg.
A solid sphere of mass m and radius r is placed inside a hollow thin spherical shell of mass M and radius R as shown in A particle of mass m' is placed on the line joining the two centres at a distance x from the point of contact of the sphere and the shell. Find the magnitude of the resultant gravitational force on this particle due to the sphere and the shell if,
- r < x < 2r.
- 2r < x < 2R.
- x > 2R.
Four particles having masses m, 2m, 3m and 4m are placed at the four corners of a square of edge a. Find the gravitational force acting on a particle of mass m placed at the centre.
Suppose the gravitational potential due to a small system is $\frac{\text{k}}{\text{r}^2}$ at a distance r from it. What will be the gravitational field? Can you think of any such system? What happens if there were negative masses?
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