Gravitational Field

Q.

The distance of the centres of moon and earth is D. The mass of earth is 81 times the mass of the moon.
At what distance from the centre of the earth, the gravitational force will be zero

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Q.

There are two bodies of masses 100 kg and 10000 kg separated by a distance 1 m. At what distance from the smaller body, the intensity of gravitational field will be zero

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Q.

A solid sphere of uniform density and radius R applies a gravitational force of attraction equal to F₁ on a particle placed at P, distance 2R from the centre O of the sphere. A spherical cavity of radius R/2 is now made in the sphere as shown in figure. The sphere with cavity now applies a gravitational force F₂ on same particle placed at P. The ratio $\frac{F_2}{F_1}$ will be

1. 1/2

2. 7/9

3. 3

4. 7

Q.

Gravitational field at the centre of semicircle formed by a thin wire AB of mass m and length l is

1. $\frac{GM}{l^2}$ along x - axis

2. $\frac{GM}{{\pi l}^2}$ along y - axis

3. $\frac{2\pi GM}{l^2}$

4. $\frac{2\pi GM}{l^2}$

Q.

Three particles each of mass m, are situated at the vertices of an equilateral triangle of side length a. The only forces acting on the particles are their mutual gravitational forces. It is desired that each particle moves in a circle while maintaining the original separation a. Find the initial velocity that should be given to each particle and also the time required for the circular motion

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Q. 85.Speed of 2cm radius ball in a viscous liquid is 20 cm/s. Then the speed of 1cm radius ball in the same liquid is (1)5 cm/s (2)10 cm/s (3)40 cm/s (4)80 cm/s Click here to view details:

Q.

Three particles A, B and C, each of mass m, are placed in a line with AB = BC = d. Find the gravitational force on a fourth particle P of same mass, placed at a distance d from the particle B on the perpendicular bisector of the line AC.

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Q. A thin spherical shell of total mass M and radius R is held fixed. A small hole is present in the shell. A mass m is released from rest at dis†an ce R from the hole. This mass subsequently moves under the gravitational force of the shell. How long does the mass will take to travel from the hole to the point daimetrically oppposite?

Q. A cylindrical vessel of radius r filled with an ideal liquid is rotating about a vertical axis. The centre of its circular base with constant angular velocity w. Find the difference in the heights of the liquid at the centre of the vessel and edge of vessel

Q. There is a uniform bar of mass m and length / hinged at centre so that it can turn in a vertical plane about a horizontal axis. Two point like masses m and 2m are rigidly attached to the ends and the arrangement is released from rest. Find initial reaction at hinge.

Q.

Three particles each of mass m, are situated at the vertices of an equilateral triangle of side length a. The only forces acting on the particles are their mutual gravitational forces. It is desired that each particle moves in a circle while maintaining the original separation a. Find the initial velocity that should be given to each particle and also the time required for the circular motion

1. $v=\sqrt{2\frac{Gm}{a}},T=2\pi (\frac{a^3}{3Gm}{)}^{\frac{1}{2}}$.

2. $v=\sqrt{\frac{Gm}{a}},T=2\pi (\frac{a^3}{3Gm}{)}^{\frac{1}{2}}$.

3. $v=\sqrt{5\frac{Gm}{a}},T=2\pi (2\frac{a^3}{3Gm}{)}^{\frac{1}{2}}$.

4. $v=\sqrt{\frac{Gm}{3a}},T=2\pi (\frac{a^3}{5Gm}{)}^{\frac{1}{2}}$.

Q. A small sphere of radius R held against the inner surface of a smooth sphericalshell of radius 6R as shown in figure. The masses of the shell and small spheresare 4M and M respectively. This arrangement is placed on a smooth horizontaltable. The small sphere is now released. The x-coordinate of the centre of theshell when the smaller sphere reaches the other extreme position is:(A) R(C) 3R(B) 2R(D) 4RX

Q.

A uniform ring of mass m is lying at a distance 1.73 a from the centre of a sphere of mass M just over the sphere where a is the small radius of the ring as well as that of the sphere. Then gravitational

force exerted is

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Q. Particle $A$ makes a perfectly elastic collision with another particle $B$ at rest. After collision, they fly apart in opposite directions with equal speeds. The ratio of masses $\frac{m_A}{m_B}$ is

1. $1:2$
2. $1:3$
3. $1:4$
4. $1:\sqrt{3}$

Q. A spherical cavity is made in a uniform solid sphereof radius R and mass M such that its surfacetouches the sphere and passes through its centre.The gravitational potential at point P will beI,

Q.

A thin spherical shell of mass M and radius R has a small hole. A particle of mass m is released at the mouth of the hole. Then

1. The particle will oscillate inside the shell, but the oscillations are not simple harmonic

2. The particle will not oscillate, but the speed of the particle will go on increasing

3. None of the above

4. The particle will execute simple harmonic motion inside the shell

Q. An object of mass $m_1$ moving horiozntally with speed $u$ collides elastically with another object of mass $m_2$ at rest. Select correct statement.

1. The momentum of the system is conserved only in direction $PQ$.
2. Momentum of $m_1$ is conserved in direction perpendicular to $SR$.
3. Momentum of $m_2$ will change in direction normal to $CR$.
4. All of these.

Q. 33. A particle is placed on the top of a hemispherical shell of same mass, Shell is free to move on the smooth ground. If particle is given a gentie push and reaches to angular position q as shown in figure then for an obsenver fixed on a shell, ratio of reaction force exerted by shell to pseudo force (as observed from shell) acting on particle, is

Q. Choose the incorrect option for elastic collision.

1. Net impulse on both the particles is zero during collision.
2. Net momentum of both particles remains conserved before and after collision in any direction even in presence of external force.
3. No component of impulse act along common tangent direction.
4. A pair of equal and opposite impulses act along common normal direction.

Q. 39. A large solid sphere of diameter d attract a small particle(mass=m) which is at distance r from center of solid sphere. If central portion of the sphere of diameter d/2 be removed leaving behind a cavity, then the new force of attraction become____.

Q.

The figure shows a spherical shell of mass M. The point A is not at the centre but away from the centre of the shell. If a particle of mass m is placed at A, then

1. It experiences a net force towards the centre

2. It experiences a net force away from centre

3. None of the above

4. It remains at rest

Q.

The distance of the centres of moon and earth is D. The mass of earth is 81 times the mass of the moon.
At what distance from the centre of the earth, the gravitational force will be zero

1. $\frac{D}{2}$

2. $\frac{2D}{3}$

3. $\frac{4D}{3}$

4. $\frac{9D}{10}$

Q. A ball collides with smooth fixed inclined plane of inclination $\theta$ after falling vertically through a distance $h\text{m}$. If it moves horizontally just after the impact, then the coefficient of restitution is

1. ${\tan }^2\theta$
2. ${\cot }^2\theta$
3. $\tan \theta$
4. $\cot \theta$

Q. Two balls $A$ and $B$ having equal masses and moving along the same straight line with velocities $+2\text{m/s}$ and $-5\text{m/s}$ respectively, collide elastically. If rightwards direction is considered as $+vex-$ axis, then their velocities after the collision will be respectively

1. $-5\text{m/s}$ and $+2\text{m/s}$
2. $3\text{m/s}$ for both
3. $5\text{m/s}$ and $1\text{m/s}$
4. None of these

Q.

A geostationary satellite

1. Revolves about the polar axis

2. Has a time period less than that of the near earth satellite

3. Moves faster than a near earth satellite

4. Is stationary in the space

Q.

The angular velocity of the earth with which it has to rotate so that acceleration due to gravity on ${60}^o$ latitude becomes zero is (Radius of earth = 640 km. At the poles g=10$m{s}^{-2}$)

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2. $7.8\times {10}^{-2}rad/sec$

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Q. 50. The volume mass density of a solid sphere is g=(G�r)/R where r is distance from centre of sphere and a R is the radius and G is constant find gravitational field intensity at the surface of solid sphere

Q. A neutron mass $1.67\times {10}^{-27}kg$ moving with a velocity $1.2\times {10}^{7}m{s}^{-1}$ collides head-on with a deuteron of mass $3.34\times {10}^{-27}kg$ initially at rest. If the collision is perfectly elastic, , what would be speed of deuteron after the collision?

1. $2\times {10}^{6}m{s}^{-1}$
2. $4\times {10}^{6}m{s}^{-1}$
3. $6\times {10}^{6}m{s}^{-1}$
4. $8\times {10}^{6}m{s}^{-1}$

Q. 49.An artificial satellite is moving around earth in a circular orbit with speed equal to one fourth of the escape speed of a body from the surface of earth.The height of satellite above earths surface is(R is radius of earth):

Q. Two balls having masses $m_1=5\text{kg}$ and $m_2=10\text{kg}$ moving with velocities $u_1=10\text{m/s}$ and $u_2=5\text{m/s}$ collide elastically. Find the change in momentum of the ball having mass $m_1$ due to collision

1. $110\text{kgm/s}$
2. $90\text{kgm/s}$
3. $-100\text{kgm/s}$
4. $50\text{kgm/s}$