CBSE Questions for Class 11 Engineering Physics Gravitation Quiz 3 - MCQExams.com

The value of gravitational constant depends upon : 
  • temperature of the atmosphere
  • masses
  • distance between the masses
  • none of these
If R$$=$$radius of the earth and g$$=$$acceleration due to gravity on the surface of the earth, the acceleration due to gravity at a distance (r>R) from the centre of the earth is proportional to
  • $$r$$
  • $$r^{2}$$
  • $$r^{-2}$$
  • $$r^{-1}$$
The height at which the value of acceleration due to gravity becomes $$50$$% of that at the surface of the earth (Radius of the earth $$ = 6400$$ km) is nearly
  • $$2650$$ km
  • $$2430$$ km
  • $$2250$$ km
  • $$2350$$ km
A missile is launched with a velocity less than the escape velocity. The sum of its kinetic and potential energies is
  • positive
  • negative
  • zero
  • may be positive or negative depending upon its initial velocity
If R$$=$$radius of the earth and g $$=$$acceleration due to gravity on the surface of the earth, the acceleration due to gravity at a distance (r<R) from the centre of the earth is proportional to
  • $$r$$
  • $$r^{2}$$
  • $$r^{-2}$$
  • $$r^{-1}$$
A man covers $$60m$$ distance in one minute on the surface of earth. The distance he will cover on the surface of moon in one minute is $$\left ( g_{m}= \dfrac{g_{e}}{6} \right )$$
  • $$60 m$$
  • $$60 X 6 m$$
  • $$\dfrac{60}{6}m$$
  • $$\sqrt{60}m$$
The depth at which the value of $$g$$ becomes $$25\%$$ of that at the surface of the earth. $$($$ Radius of the earth $$=$$ 6400km.$$)$$
  • 4800 km
  • 2400 km
  • 3600 km
  • 1200 km
A body has weight (W) on the ground. The work which must be done to lift it to a height equal to the radius of the earth, R, is
  • equal to W $$\times$$ R
  • greater than W $$\times$$ R
  • less than W $$\times$$ R
  • Cannot be determined
The ratio of the radius of a planet A to that of planet B is $$r$$. The ratio of accelerations due to gravity for the two planets is $$x$$. The ratio of the escape velocities from the two planets is :
  • $$\sqrt{rx}$$
  • $$\sqrt{\dfrac{r}{x}}$$
  • $$\sqrt{r}$$
  • $$\sqrt{\dfrac{x}{r}}$$
The ratio of acceleration due to gravity at a depth $$h$$ below the surface of earth and at a height $$h$$ above the surface for $$h<<R$$
  • is constant.
  • increases linearly with h.
  • varies parabolically with h.
  • decreases.
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 of B goes on increasing
  • B goes on decreasing and that of A goes on increasing
  • each decreases at the same rate
  • each decreases at different rates
The acceleration due to gravity on the surface of moon is $$1/6$$ that on the earth and the diameter of the earth is $$4$$ times the diameter of the moon. The rough ratio of the escape velocity of the moon to that of the earth is
  • $$1 : 4$$
  • $$4 : 1$$
  • $$5 : 1$$
  • $$1 : 5$$
If the radius of earth decreases by $$10\%$$, the mass remaining unchanged, then the acceleration due to gravity
  • decreases by $$19\%$$
  • increases by $$19\%$$
  • decreases by more than $$19\%$$
  • increases by more than $$19\%$$
What is the escape velocity from the surface of the earth of radius $$R$$ and density $$\rho $$ ?
  • $$2R\sqrt{\dfrac{2\pi \rho G}{3}}$$
  • $$2\sqrt{\dfrac{2\pi \rho G}{3}}$$
  • $$2\pi \sqrt{\dfrac{R}{g}}$$
  • $$\sqrt{\dfrac{2\pi G\rho }{R^{2}}}$$
The ratio of the radii of planets A and B is $$K_{1}$$ and ratio of accelerations due to gravity on them is $$K_{2}$$ The ratio of escape velocities from them will be:
  • $$K_{1}K_{2}$$
  • $$\sqrt{K_{1}K_{2}}$$
  • $$\sqrt{\dfrac{K_{1}}{K_{2}}}$$
  • $$\sqrt{\dfrac{K_{2}}{K_{1}}}$$
A spaceship is launched into a circular orbit of radius $$R$$ close to the surface of earth. The additional velocity to be imparted to the spaceship in the orbit to overcome the earth's gravitational pull is : $$($$ $$g =$$ acceleration due to gravity $$)$$
  • $$1.414Rg$$
  • $$1.414\sqrt{Rg}$$
  • $$0.414Rg$$
  • $$0.414\sqrt{gR}$$
A particle hanging from a spring stretches it by $$1 cm$$ at earth's surface. Radius of earth is $$6400 km$$. At a place $$800 km$$ above the earths surface, the same particle will stretch the spring by
  • $$0.79 cm$$
  • $$1.2 cm$$
  • $$4 cm$$
  • $$17 cm$$
If the radius of earth were to shrink by one percent, its mass remaining the same, the acceleration due to gravity on the earth's surface would
  • decrease
  • remain unchanged
  • increase
  • nothing will happen
A tunnel is dug along a diameter of the Earth. The force on a particle of mass $$m$$ placed in the tunnel at a distance $$x$$  from the centre is:
  • $$\dfrac{GM_{e}m}{R^{3}}x$$
  • $$\dfrac{GM_{e}m}{R^{2}}x$$
  • $$\dfrac{GM_{e}m}{R^{3}x}$$
  • $$\dfrac{GM_{e}mR^{3}}{x}$$
A space craft is launched in a circular orbit very close to the earth. What additional velocity should be given to the space craft so that it might escape the earth's gravitational pull:
  • $$20.2 Kms^{-1}$$
  • $$3.25 Kms^{-1}$$
  • $$8 Kms^{-1}$$
  • $$11.2 Kms^{-1}$$
If $$R$$ is radius of the earth and $$W$$ is work done in lifting a body from the ground to an altitude $$R$$, the work which should be done in lifting it further to twice that altitude is:
  • $$\dfrac{W}{2}$$
  • $$W$$
  • $$\dfrac{W}{3}$$
  • $$3W$$
A body of mass $$m$$ is raised from the surface of the earth to a height $$nR$$ ($$R$$-radius of earth). Magnitude of the change in the gravitational potential energy of the body is ($$g$$- acceleration due to gravity on the surface of earth) :
  • $$\left ( \dfrac{n}{n+1} \right )mgR$$
  • $$\left ( \dfrac{n-1}{n} \right )mgR$$
  • $$\dfrac{mgR}{n}$$
  • $$\dfrac{mgR}{\left ( n-1 \right )}$$
The work done to increase the radius of orbit of a satellite of mass $$m$$ revolving around a planet of mass $$M$$ from orbit of radius $$R$$ into another orbit of radius $$3R$$ is :
  • $$\dfrac{2GMm}{3R}$$
  • $$\dfrac{GMm}{R}$$
  • $$\dfrac{GMm}{6R}$$
  • $$\dfrac{GMm}{24R}$$
Energy required to move a body of mass m from an orbit of radius 2R to 3R is:
  • $$\dfrac{GMm}{12R^{2}}$$
  • $$\dfrac{GMm}{3R^{2}}$$
  • $$\dfrac{GMm}{8R}$$
  • $$\dfrac{GMm}{6R}$$
If $$g$$ is acceleration due to gravity on the earth's surface, the gain in the potential energy of an object of mass $$m$$  raised from the surface of the earth to a height equal to the radius $$R$$  of the earth is:
  • $$2 mgR$$
  • $$mgR$$
  • $$\dfrac{mgR}{4}$$
  • $$\dfrac{mgR}{2}$$
The gravitational P.E. of a rocket of mass 100 kg at a distance of $$10^{7}$$ m from the earths centre is $$-4\times 10^{9}$$   J. The weight of the rocket at a distance of $$10^{9}$$ m from the centre of the earth is :
  • $$4\times 10^{-2}$$ N
  • $$4\times 10^{-9}$$ N
  • $$4\times 10^{-6}$$ N
  • $$4\times 10^{-3}$$ N
The angular velocity of rotation of a star (mass M and radius R), such that the matter will start escaping from its equator is:
  • $$\sqrt{\dfrac{2GR}{M}}$$
  • $$\sqrt{\dfrac{2GM}{R^{3}}}$$
  • $$\sqrt{\dfrac{2GM}{R}}$$
  • $$\sqrt{\dfrac{2GM^{2}}{R}}$$
A small body is initially at a distance $$r$$ from the centre of earth. $$r$$ is greater than the radius of the earth. If it takes $$W$$ joules of work to move the body from this position to another position at a distance $$2r$$ measured from the centre of earth, then how many joules would be required to move it from this position to a new position at a distance of $$3r$$ from the centre of the earth.
  • $$\dfrac{W}{5}$$
  • $$\dfrac{W}{3}$$
  • $$\dfrac{W}{2}$$
  • $$\dfrac{W}{6}$$
If $$g$$ is the acceleration due to gravity on the earth's surface, the gain in the potential energy of an object of mass $$m$$ raised from the surface of the earth to a height equal to the radius $$R$$ of the earth is
  • $$2mgR$$
  • $$\dfrac{1}{2}mgR$$
  • $$\dfrac{1}{4}mgR$$
  • $$mgR$$
A person bring a mass of $$1 kg$$ from infinite to point $$A$$. Initially the mass was at rest but is moves a speed of $$2 m /s$$ as it reaches to $$A$$. The workdone by the person on mass is $$-3 J$$ the gravitational potential at $$A$$ is
  • $$-3 J / kg$$
  • $$-2 J / kg$$
  • $$-5 J / kg$$
  • $$-7 J / kg$$
The change in the P.E., when a body of mass $$m$$ is displaced from Earth's surface to a vertical height equal to radius of earth (g $$=$$ acceleration due to gravity on earth surface) is:
  • $$\dfrac{mgR}{2}$$
  • $$\dfrac{2mgR}{3}$$
  • $$\dfrac{3mgR}{4}$$
  • $$\dfrac{mgR}{3}$$
What is the minimum energy required to launch a satellite of mass $$m$$ from the surface of a planet of mass $$M$$ and radius $$R$$ in a circular orbit at an altitude of $$2R$$?
  • $$\displaystyle \frac{2GmM}{3R}$$
  • $$\displaystyle \frac{GmM}{2R}$$
  • $$\displaystyle \frac{GmM}{3R}$$
  • $$\displaystyle \frac{5GmM}{6R}$$
A sky laboratory of mass $$2\times 10^{3}Kg$$ is raised from a circular orbit of radius 2R to a circular orbit of radius 3R. The work done is (approximately):
  • $$10^{16}J$$
  • $$2\times 10^{10}J$$
  • $$10^{6}J$$
  • $$3\times 10^{10}J$$
A particle of mass M is situated at the centre of a spherical shell of same mass and radius a. The magnitude of the gravitational potential at a point situated at a/2 distance from the centre will be :
  • $$\frac{GM}{a}$$
  • $$\frac{2GM}{a}$$
  • $$\frac{3GM}{a}$$
  • $$\frac{4GM}{a}$$
A particle of mass M is situated at the center of a spherical shell of same mass and radius a. The gravitational potential at a point situated at $$\frac{a}{2}$$ distance from the centre, will be
  • $$-\frac{3GM}{a}$$
  • $$-\frac{2GM}{a}$$
  • $$-\frac{GM}{a}$$
  • $$-\frac{4GM}{a}$$
The kinetic energy needed to project a body of mass $$m$$ from the earth surface to infinity is
  • $$\dfrac{1}{2}$$mgR
  • $$2 mgR$$
  • $$mgR$$
  • $$\dfrac{1}{4}$$mgR
A satellite of mass $$m$$ moves along an elliptical path around the earth. The areal velocity of the satellite is proportional to
  • $$m$$
  • $$m^{-1}$$
  • $$m^{0}$$
  • $$m^{\frac{1}{2}}$$
If $$V_{e}$$ is the escape velocity of a body from a planet of mass M and radius R. Then the velocity of the satellite revolving at height h from the surface of the planet will be:
  • $$V_{e}\sqrt{\dfrac{R}{R+h}}$$
  • $$V_{e}\sqrt{\dfrac{2R}{R+h}}$$
  • $$V_{e}\sqrt{\dfrac{R+h}{R}}$$
  • $$V_{e}\sqrt{\dfrac{R}{2\left ( R+h \right )}}$$
The height at which the acceleration due to gravity becomes $$\displaystyle \frac{\mathrm{g}}{9}$$ (where $$\mathrm{g}=$$ the acceleration due to gravity on the surface of the earth) in terms of $$\mathrm{R}$$, the radius of the earth, is: 
  • $$2\ \mathrm{R}$$
  • $$\displaystyle \frac{\mathrm{R}}{\sqrt{2}}$$
  • $$\mathrm{R}/2$$
  • $$\sqrt{2}\ \mathrm{R}$$
The ratio of Earth's orbital angular momentum (about the sun) to its mass is $$4.4 \times 10^{15}\ m^{2}\ s^{-1}$$. The area enclosed by the earth's orbit is approximately
  • $$1 \times 10^{22}\ m^{2}$$
  • $$3 \times 10^{22}\ m^{2}$$
  • $$5 \times 10^{22}\ m^{2}$$
  • $$7 \times 10^{22}\ m^{2}$$
At what height, is the value of g half that on the surface of earth? (R = radius of the earth)
  • 0.414R
  • R
  • 2R
  • 3.5R
Experimental value of G is
  • $$6.67\times 10^{-11} Nm^2/kg^2$$
  • $$66.7\times 10^{-11} Nm^2/kg^2$$
  • $$667\times 10^{-11} Nm^2/kg^2$$
  • None of these
Maximum weight of a body is
  • at the center of the earth.
  • inside the earth.
  • on the surface of the earth.
  • above the surface of earth.
The weight of an object in the coal mine, sea level and at the top of the mountain are respectively  $$\omega_1 , \omega_2, \omega_3$$ then
  • $${\omega}_1 < {\omega}_2 > {\omega}_3$$
  • $${\omega}_1 = {\omega}_2 = {\omega}_3$$
  • $${\omega}_1 < {\omega}_2 < {\omega}_3$$
  • $${\omega}_1 > {\omega}_2 > {\omega}_3$$
At a place, the value of 'g' is less by 1% than its value on the surface of the Earth (Radius of Earth, $$R=6400 km$$). The place is :
  • 64 km below the surface of the earth
  • 64 km above the surface of the earth
  • 30 km above the surface of the earth
  • 32 km below the surface of the earth
Depth from the surface of the earth at which is acceleration due to gravity is 25% of acceleration due to gravity at the surface
  • 1200 km
  • 4000 km
  • 3600 km
  • 4800 km
A body of mass 'm' is taken from the earth's surface to the height equal to twice the radius (R) of the earth. The change in potential energy of body will be -
  • mg 2R
  • $$\displaystyle \frac{2}{3}mgR$$
  • 3 mgR
  • $$\displaystyle \frac{1}{3}mgR$$
The weight of an object at the centre of the earth of radius R is
  • zero
  • infinite
  • $$R$$ times the weight at the surface of the earth
  • $$1/R^{2}$$ times the weight at surface of the earth
A man weighs $$60 kg$$ at earth's surface. At what height above the earth's surface his weight becomes $$30 kg$$? (radius of earth  $$=6400 km$$).
  • $$1624 km$$
  • $$2424 km$$
  • $$2624 km$$
  • $$2826 km$$
The variation of g  with height or depth (r) is shown correctly by the graph in the figure (where R = radius of the earth),
0:0:1


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