CBSE Questions for Class 11 Engineering Physics Gravitation Quiz 13 - MCQExams.com

A particle hanging from a massless spring stretches it by 2 cm at earths surface. How much will the same particle stretch the spring at a height of 2624 km from the surface of the earth? (Radius of earth $$=$$ 6400 km).
  • $$1 cm$$
  • $$2 cm$$
  • $$3.3 cm$$
  • $$4 cm$$
If $$v_{e}$$ is escape velocity and $$v_{0}$$  is orbital velocity of a satellite for orbit close to the earth's surface, then these are related by:
  • $$v_{0}=v_{e}$$
  • $$v_{e}=\sqrt{2v_{0}}$$
  • $$v_{e}=\sqrt{2}v_{0}$$
  • $$v_{0}=\sqrt{2}v_{e}$$
Three planets of same density and with radii $$\mathrm{R}_{1}, \mathrm{R}_{2}$$ and $$\mathrm{R}_{3}$$, such that $$\mathrm{R}_{1}=2\mathrm{R}_{2}=3\mathrm{R}_{3},$$ have gravitation fields on the surfaces $$\mathrm{E}_{1}, \mathrm{E}_{2}, \mathrm{E}_{3}$$ and escape velocities $$\mathrm{v}_{1}, \mathrm{v}_{2}, \mathrm{v}_{3}$$ respectively, Then
  • $$\displaystyle \frac{\mathrm{E}_{1}}{\mathrm{E}_{2}}=\frac{1}{2}$$
  • $$\displaystyle \frac{\mathrm{E}_{1}}{\mathrm{E}_{3}}=3$$
  • $$\displaystyle \frac{\mathrm{v}_{1}}{\mathrm{v}_{2}}=2$$
  • $$\displaystyle \frac{\mathrm{v}_{1}}{\mathrm{v}_{3}}=\frac{1}{3}$$
 A spherical $$\Uparrow \mathrm{o}\mathrm{l}\mathrm{e}$$ of radius $$\mathrm{R}/2$$ is excavated from $$\mathrm{t}\Uparrow \mathrm{e}$$ asteroid of mass
$$\mathrm{M}$$ as shown in fig. $$\mathrm{T}\Uparrow \mathrm{e}$$ gravitational acceleration at a point on $$\mathrm{t}\Uparrow \mathrm{e}$$
surf ace of $$\mathrm{t}\Uparrow \mathrm{e}$$ asteroid just above $$\mathrm{t}\Uparrow \mathrm{e}$$ excavation is :

42020_d7df8088d76d415c88e236c0771cf2e6.png
  • $$\mathrm{G}\mathrm{M}/\mathrm{R}^{2}$$
  • $$\mathrm{G}\mathrm{M}/2\mathrm{R}^{2}$$
  • $$\mathrm{G}\mathrm{M}/8\mathrm{R}^{2}$$
  • $$7\mathrm{g}\mathrm{W}8\mathrm{R}^{2}$$
A body of mass m is placed on earth surface which is taken from earth surface to a height of $$h = 3R$$ then change in gravitational potential energy is:
  • $$\dfrac{mgR}{4}$$
  • $$\dfrac{2}{3}mgR$$
  • $$\dfrac{3}{4}mgR$$
  • $$\dfrac{mgR}{2}$$
A particle starts from rest at a distance $$\mathrm{R}$$ from the  centre and along the axis of a fixed ring of radius $$\mathrm{R}$$ a mass M. Its velocity at the  centre of the ring is: 


42036.jpg
  • $$\sqrt{\frac{\sqrt{2}\mathrm{G}\mathrm{M}}{\mathrm{R}}}$$
  • $$\sqrt{\frac{2\mathrm{G}\mathrm{M}}{\mathrm{R}}}$$
  • $$\sqrt{(1-\frac{1}{\sqrt{2}})\frac{\mathrm{G}\mathrm{M}}{\mathrm{R}}}$$
  • $$\sqrt{(2-\sqrt{2})\frac{\mathrm{G}\mathrm{M}}{\mathrm{R}}}$$
A spherical ball is dropped in a long column of viscous liquid. Which of the following graphs represent the variation of
i) The gravitational force with time
ii) The viscous force with time
iii) The net force acting on the ball with time
73630.png
  • Q, R, P
  • R, Q, P
  • P, Q, R
  • R, P, Q
 lf $$\mathrm{W}_{1},\ \mathrm{W}_{2}$$ and $$\mathrm{W}_{3}$$ represent the work done in moving a particle from A to $$\mathrm{B}$$ along three different paths 1, 2 and 3 respectively (as shown) in the gravitational field of a point mass $$\mathrm{m}$$, find the correct relation between $$\mathrm{W}_{1},\ \mathrm{W}_{2}$$ and $$\mathrm{W}_{3}$$.

42936.jpg
  • $$\mathrm{W}_{1}>\mathrm{W}_{2}>\mathrm{W}_{3}$$
  • $$\mathrm{W}_{1}=\mathrm{W}_{2}=\mathrm{W}_{3}$$
  • $$\mathrm{W}_{1}<\mathrm{W}_{2}<\mathrm{W}_{3}$$
  • $$\mathrm{W}_{2}>\mathrm{W}_{1}>\mathrm{W}_{3}$$
Acceleration due to gravity as a function of $$r$$ is given by
  • $$\dfrac{4}{3}\pi Gr(A-BR)$$
  • $$4\pi Gr(A-BR)$$
  • $$\dfrac{4}{3}\pi Gr(A-\dfrac{3}{4}BR)$$
  • $$\dfrac{4}{3}\pi Gr\left ( A-\dfrac{4}{3}BR \right )$$
Find the distance between the centre of gravity and centre of mass of a two-particle system attached to the ends of a light rod. Each particle has the same mass. Length of the rod is $$R$$, where $$R$$ is the radius of the earth.

42028_030fb193362844b19fff2f4d05ba1d41.png
  • $$R$$
  • $$\dfrac{R}{2}$$
  • zero
  • $$\dfrac{R}{4}$$
Consider the following statements about acceleration due to gravity on earth and mark the correct statement(s) :
  • The value of $$g$$ is constant throughout
  • $$g' = g(1 - \dfrac {d}{r})$$
  • $$g$$ is slightly less (by about $$1$$%) when distance $$< 200 m$$
  • $$g$$ is slightly greater when distance $$< 200 m$$
The angular velocity of rotation of the earth in order to make the effective acceleration due to gravity equal to zero at equator should be $$g=10m/s^2, R=6400 km$$.
  • $$2.15\times 10^3$$ rad/sec
  • $$2.25\times 10^{-3}$$ rad/sec
  • $$1.25\times 10^3$$ rad/sec
  • $$1.25\times 10^{-3}$$ rad/sec
The ratio of the radii of the planets $$P_{1}$$ and $$P_{2}$$ is $$k_{1}.$$ The corresponding ratio of the acceleration due to the gravity on them is $$k_{2}.$$ The ratio of the escape velocities from them will be
  • $$k_{1}k_{2}$$
  • $$\sqrt{k_{1}k_{2}}$$
  • $$\sqrt{(k_{1}/k_{2})}$$
  • $$\sqrt{(k_{2}/k_{1})}$$
A planet is revolving in an elliptical orbit around the sun as shown in figure.The areal velocity (area swapped by the radius vector with respect to sun in unit time) is :
74130.jpg
  • $$\dfrac{1}{4}\left ( r_{1}+r_{2} \right )v_{1}$$
  • $$\dfrac{1}{2}r_{2}v_{2}$$
  • $$\dfrac{1}{2}\dfrac{v_{1}r{_{1}}^{2}}{r_{2}}$$
  • dependent on the position of planet from sun
Acceleration due to gravity as a function of $$r$$ is given by :
  • $$\dfrac {4}{3} \pi Gr (A - Br)$$
  • $$4 \pi Gr (A - Br)$$
  • $$\dfrac {4}{3} \pi Gr (A - \dfrac {3}{4} Br)$$
  • $$\dfrac {4}{3} \pi Gr (A - \dfrac {3}{2} Br)$$
A planet of radius $$R =1/10 \times {(radius \quad of \quad earth)}$$ has the same mass density as Earth. Scientist dig a well of depth $$\dfrac{R}{5}$$ on it and lower a wire of the same length and of linear mass density $$10^{-3} kgm^{-3}$$ into it. If the wire is not touching anywhere, the force applied at the top of the wire by a person holding it in places is (take the radius of earth $$ = 6\times 10^6$$ and the acceleration due to gravity on earth is $$10ms^{-2}$$)
  • $$96 N$$
  • $$108 N$$
  • $$120 N$$
  • $$150 N$$
The ratio of the earth's orbital angular momentum (about the Sun) to its mass is $$4.4\times 10^{15} m^2s^{-1}$$. The area enclosed by the earth's orbit is approximately $$\underline{\hspace{0.5in}} m^2$$.
  • $$6.94\times 10^{22} m^2$$
  • $$4.24\times 10^{22} m^2$$
  • $$4.92\times 10^{22} m^2$$
  • $$5.54\times 10^{22} m^2$$
If the change in the value of $$g$$ at a height $$h$$ above the surface of the earth is the same as at a depth $$x$$ below it when both $$x$$ and $$h$$ are much smaller than the radius of the earth, then
  • $$x = h$$
  • $$x = 2h$$
  • $$x = \dfrac{h}{2}$$
  • $$x = \dfrac{h}{3}$$
Calculate energy needed for moving a mass of $$4kg$$ from the centre of the earth to its surface (in joule). If radius of the earth is 6400 km and acceleration due to gravity at the surface of the earth is
$$g = 10 m/sec^2$$
  • $$1.28 \times 10^8 J$$
  • $$1.28 \times 10^6 J$$
  • $$2.56 \times 10^8 J$$
  • $$2.56 \times 10^10 J$$
The mass of the Jupiter is $$1.9\times 10^{27}\ kg$$ and that of the sun is $$1.99\times 10^{38}\ kg$$. The mean distance of the Jupiter from the sun is $$7.8\times 10^{11}\ m$$. Speed of the Jupiter is (assuming that Jupiter moves in a circular orbit around the sun)
  • $$1.304\times 10^4\ m/sec$$.
  • $$13.04\times 10^4\ m/sec$$.
  • $$1.304\times 10^6\ m/sec$$.
  • $$1.304\times 10^2\ m/sec$$.
A space ship is launched into a circular orbit close to the surface of the earth. The additional velocity now imparted to the spaceship in the orbit to overcome the gravitational pull is 
  • $${ 11.2 }km{ s }^{ -1 }$$
  • $${ 8 }km{ s }^{ -1 }$$
  • $${ 3.2 }km{ s }^{ -1 }$$
  • $${ 1.414 }\times { 8 }km{ s }^{ -1 }$$
Find approximately the third cosmic velocity $$v_3$$ in km/s i.e. the minimum velocity that has to be imparted to a body relative to the Earth's surface to drive it out of the Solar system. It is given that the rotation of the Earth about its own axis is to be neglected.
  • $$16.6$$
  • $$20$$
  • $$10$$
  • None of these
A particle would take time $$t_1$$ to move down a straight tube from the surface of earth (supposed to be homogeneous sphere) to its centre. If gravitational acceleration were to remain constant, time would be $$t_2$$. The ratio $$t/t'$$ will be
  • $$\displaystyle \frac{\pi}{2 \sqrt{2}}$$
  • $$\displaystyle \frac{\pi}{2}$$
  • $$\displaystyle \frac{2\pi}{3}$$
  • $$\displaystyle \frac{\pi}{\sqrt{3}}$$
Which of the following is correct?
  • The value of g is constant throughout
  • $$\displaystyle g \propto \frac{1}{r^2}$$
  • $$g$$ is slightly less (by about 1%) when distance $$< 200 m$$
  • $$g$$ is slightly greater when distance $$< 200 m$$.
The largest and the shortest distance of the earth from sun are a and b, respectively. The distance of the earth from sun when it is at a point where perpendicular drawn from the sun on the major axis meets the orbit is
  • $$\displaystyle \frac{ab}{a + b}$$
  • $$\displaystyle \frac{ab}{2(a + b)}$$
  • $$\displaystyle \frac{2ab}{a+b}$$
  • $$\displaystyle \frac{a+b}{2ab}$$
The maximum vertical distance through which a fully dressed astronaut can jump on the earth is $$0.5 m$$.  If mean density of the Moon is two-third that of the earth and radius is one quarter that of the earth, the maximum vertical distance which he can jump on the Moon and the ratio of the time of duration of the jump on the Moon to hold on the earth are
  • $$3 m$$, $$6:1$$
  • $$6 m$$, $$3:1$$
  • $$3 m$$, $$1:6$$
  • $$6 m$$, $$1:6$$
If $$V_e$$ is the escape velocity of a body from a planet of mass $$M$$ and radius $$R$$. Then, the velocity of satellite revolving at height $$h$$ from the surface of planet will be
  • $$V = V_e \sqrt{\dfrac{R}{(R + h)}}$$
  • $$V = V_e \sqrt{\dfrac{2R}{(R + h)}}$$
  • $$V = V_e \sqrt{\dfrac{(R + h)}{R}}$$
  • $$V = V_e \sqrt{\dfrac{R}{ 2 (R + h)}}$$
A tunnel is dug along a chord of the earth at a perpendicular distance $$\displaystyle \frac{R}{3}$$ from the earth's centre. Assume wall of the tunnel is frictionless. Find the force exerted by the wall on mass m at a distance x from the centre of the tunnel

143669.jpg
  • $$\displaystyle \frac{mg \sqrt{\frac{R^2}{9} + x^2}}{R}$$
  • $$\displaystyle \frac{mg x}{\sqrt{R^2 / a + x^2}}$$
  • $$\displaystyle \frac{mg}{3}$$
  • $$\displaystyle \frac{mg x}{R}$$
Four equal masses (each of mass $$M$$) are placed at the corners of a square of side $$a$$. The escape velocity of a body from the centre $$O$$ of the square is
  • $$\displaystyle \sqrt[4] {\frac {2GM}{a}}$$
  • $$\displaystyle \sqrt {\frac {8\sqrt {2}GM}{a}}$$
  • $$\displaystyle \frac {4GM}{a}$$
  • $$\displaystyle \sqrt {\frac {4\sqrt {2}GM}{a}}$$
Let $$V$$ and $$E$$ denote the gravitational potential and gravitational field at a point, respectively. It is possible to have
  • $$V=0$$ and $$E=0$$
  • $$V=0$$ and $$E\ne 0$$
  • $$V\ne 0$$ and $$E=0$$
  • $$V\ne 0$$ and $$E\ne 0$$
Which of the following statements are true about acceleration due to gravity?
  • $$g$$ decreases in moving away from the centre if $$r>R$$
  • $$g $$ decreases in moving away from the centre if $$r<R$$
  • $$g$$ is zero at the centre of the earth
  • $$g$$ decreases if earth stops rotating on its axis
A body of mass $$m$$ is taken from earth's surface to the height equal to the radius of earth, the change in potential energy will be of
  • $$\displaystyle mgR_e$$
  • $$\displaystyle mgR_e/2$$
  • $$\displaystyle 2mgR_e$$
  • $$\displaystyle mgR_e/4$$
A tunnel is dug along a chord of the earth at a perpendicular distance $$R/2$$ from the earth's centre. The wall of the tunnel may be assumed to be frictionless. A particle is released from one end of the tunnel. The pressing force by the particle on the wall, and the acceleration of the particle vary with $$x$$ (distance of the particle from the centre) according to
A tunnel is dug along a chord of the earth at a perpendicular distance $$R/2$$ from the earth's centre. The wall of the tunnel may be assumed to be frictionless. A particle is released from one end of the tunnel. The pressing force by the particle on the wall and the acceleration of the particle varies with $$x$$ (distance of the particle from the centre) according to :
A (nonrotating) star collapses onto itself from an initial radius $$R_1$$ with its mass remaining unchanged. Which curves in figure best describes the gravitational acceleration $$a_g$$ on the surface of the star as a function of the radius of the star during the collapse
194793.png
  • $$\displaystyle a$$
  • $$\displaystyle b$$
  • $$\displaystyle c$$
  • $$\displaystyle d$$
Suppose, the acceleration due ot gravity at the earth's surface is $$10 m s^{-2}$$ and at the surface of Mars it is $$4.0ms^{-2}$$. A $$60$$kg passenger goes from the Earth to the Mars in a spaceship moving with a constant velocity. Neglect all other objects in the sky. Which part of figure bests represents the weight (net gravitational force) of the passenger as a function of time?
192171_ca07da6b625e434f984c116e4c037627.png
  • $$\displaystyle A$$
  • $$\displaystyle B$$
  • $$\displaystyle C$$
  • $$\displaystyle D$$
A tunnel is dug along a diameter of the earth. If $${ M }_{ e }$$ and $${ R }_{ e }$$ are the mass and radius, respectively, of the earth, then the force on a particle of mass $${ m }$$ placed in the tunnel at a distance $${ r }$$ from the centre is :
  • $$\displaystyle \cfrac { { G }{ M }_{ e }{ m } }{ { R }_{ e }^{ 3 } } { r }$$
  • $$\displaystyle \frac { { G }{ M }_{ e }{ m } }{ { R }_{ e }^{ 3 }{ r } }$$
  • $$\displaystyle \frac { { G }{ M }_{ e }{ m }{ R }_{ e }^{ 3 } }{ r }$$
  • $$\displaystyle \cfrac { { G }{ M }_{ e }{ m } }{ { R }_{ e }^{ 2 } } { r }$$
A person brings amass of $$1 kg$$ from infinity to a point A lnitially, the mass was at rest but it moves at a speed of $$3 m/s$$ as it reaches A. The work done by the person on the mass is $$- 5.5 J$$ The gravitational potential at $$A$$ is
  • $$-1J/kg$$
  • $$-4.5 J/kg$$
  • $$-5.5J /kg$$
  • $$-10J/kg$$
The ratio of SI units to CGS units of g is.
  • $$10^2$$
  • 10
  • $$10^{-1}$$
  • $$10^{-2}$$
Escape velocity for a projectile at earth's surface is $$v_e$$. A body is projected form earth's surface with velocity $$2_{v_e}$$. The velocity of the body when it is at infinite distance from the centre of the earth is 
  • $$v_e$$
  • $$2v_e$$
  • $$\sqrt 2 v_e$$
  • $$\sqrt 3 v_e$$
If the gravitational acceleration at surface of earth is $$ g$$, then increase in potential energy in lifting an object of mass $$m$$ to a height equal to the radius $$R$$ of earth will be.
  • $$\dfrac {mgR}{2}$$
  • $$2mgR$$
  • $$mgR$$
  • $$\dfrac {mgR}{4}$$
Maximum weight of a body is.
  • At the centre of the earth
  • Inside the earth
  • On the surface of the earth
  • Above the surface of earth
Read the assertion and reason carefully to mark the correct option out of the options given below :

Assertion : At height $$h$$ from ground and at depth $$h$$ below ground, where h is approximately equal to $$0.62 R$$, the value of $$g$$ acceleration due to gravity is same.

Reason : Value of $$g$$ decreases both sides, in going up and down.
  • If both assertion and reason are true and the reason is the correct explanation of the assertion
  • If both assertion and reason are true but reason is not the correct explanation of the assertion
  • If assertion is true but reason is false
  • If assertion is false but reason is true
The density of the core of a planet is $$P_{1} $$ and that of the outer shell is $$P_{2}$$ the radii of the core and that of the planet are $$R$$ and $$2R$$ respectively. The acceleration due to gravity at the surface of the planet is same as at depth $$R$$. Find the ratio of $$\displaystyle \frac{P_{1}}{P_{2}}$$

219944_f3df74711eb046739cf088ff96599827.png
  • $$7:3$$
  • $$3:7$$
  • $$7:4$$
  • $$4:7$$
There are two planets. The ratio of radius of the two planets is $$k$$ but ratio of acceleration due to gravity of both planets is $$g$$. What will be the ratio of their escape velocity?
  • $$(kg)^{1/2}$$
  • $$(kg)^{-1/2}$$
  • $$(kg)^{2}$$
  • $$(kg)^{-2}$$
Suppose a vertical tunnel is dug along the diameter of the earth, assumed to be a sphere of uniform mass density $$\rho$$. If a body of mass $$m$$ is thrown in this tunnel, its acceleration at a distance $$y$$ from the centre is given by:
219905_4d81c080bc754d7496e419e1fe5cb7a2.png
  • $$\displaystyle \frac{4\pi}{3}G\rho ym$$
  • $$\displaystyle \frac{3}{4}\pi \rho y$$
  • $$\displaystyle \frac{4}{3}\pi \rho y$$
  • $$\displaystyle \frac{4}{3}\pi G\rho y$$
The gravitational potential difference between the surface of a planet and a point $$20 m$$ above it is $$16 J/kg$$. Then the work done in moving a $$2 kg$$ mass by $$8 m$$ on a slope $$60$$ degree from the horizontal, is:
  • $$11.1 J$$
  • $$5.55 J$$
  • $$16 J$$
  • $$27.7 J$$
Imagine a spacecraft going from the earth to the moon. How does its weight vary as it goes from the earth to the moon?
  • Initially decreases then becomes zero and again increases.
  • Initially increases and again increases.
  • Initially decreases again increases.
  • zero throughout the path
At what height in km over the earth's pole the free fall acceleration decreases by one percent? (Assume the radius of the earth to be $$6400\ km$$)
  • $$32$$
  • $$64$$
  • $$80$$
  • $$1.253$$
A body hanging from a massless spring stretches it by $$3$$cm on Earth's surface. At a place $$800$$km above the Earth's surface, the same body will stretch the spring by : (Radius of Earth $$=6400$$km)
  • $$\left(\displaystyle\frac{34}{27}\right)$$cm
  • $$\left(\displaystyle\frac{64}{27}\right)$$cm
  • $$\left(\displaystyle\frac{27}{64}\right)$$cm
  • $$\left(\displaystyle\frac{27}{34}\right)$$cm
  • $$\left(\displaystyle\frac{35}{81}\right)$$cm
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