CBSE Questions for Class 11 Engineering Physics Gravitation Quiz 6 - MCQExams.com

A body of mass $$m$$ is lifted up from the surface of earth to a height three times the radius of the earth $$R$$.The change in potential energy of the body is
  • $$3mgR$$
  • $$\displaystyle\frac{5}{4}mgR$$
  • $$\displaystyle\frac{3}{4}mgR$$
  • $$2mgR$$
At some planet '$$g$$' is $$1.96 m/s^2$$. If it is safe to jump from a height of $$2m$$ on earth, then what should be corresponding safe height for jumping on that planet
  • $$5m$$
  • $$2m$$
  • $$10m$$
  • $$20m$$
On the surface of earth acceleration due to gravity is g and gravitational potential is V.
Column-IColumn-II
a) At height h = R, value of g(p) decreases by a factor 1/4
(b) At depth h = R/2 value of g(q) decreases by a factor 1/2
(c) At height h = R, of V(r) Increases by a factor 11/8
(d) At depth h = R/2 of V (s) Increases by a factor 2
(t) None

  • (a - p), (b - q), (c - s), (d - t)
  • (a - q), (b - p), (c - t), (d - s)
  • (a - t), (b - s), (c - p), (d - q)
  • None of these
If velocity of a satellite is half of escape velocity, then distance of the satellite from earth surface will be.
  • $$6400 km$$
  • $$12800 km$$
  • $$6400 \sqrt 2 km$$
  • $$\dfrac {6400}{\sqrt 2}km$$
Mass of a planet is $$5 \times  10^{24}$$ kg and radius is $$6.1 \times  10^6$$m. The energy needed to send a $$2$$ kg body into space from its surface, would be.
  • $$9$$ joule
  • $$18$$ joule
  • $$2.2 \times 10^8 $$joule
  • $$1.1 \times 10^8 $$joule
Gravitational potential difference between surface of a planet and a point situated at a height of $$20m$$ above its surface is $$2 joule/kg$$. If gravitational field is uniform, then the work done in taking a $$5kg$$ body of height $$4$$ meter above surface will be :-
  • $$2J$$
  • $$20J$$
  • $$40J$$
  • $$10J$$
Potential energy of a $$3 kg$$ body at the surface of a planet is $$54J$$ then escape velocity will be.
  • $$18 m/s$$
  • $$162 m/s$$
  • $$36 m/s$$
  • $$6 m/s$$
An object weighs $$10 N$$ at the north pole of theearth. In a geostationary satellite distance $$7R$$ from the centre of the earth (of radius $$R$$), the true weight and the apparent weight are.
  • $$0 N, 0 N$$
  • $$0.2 N, 0 N$$
  • $$0.2 N, 9.8 N$$
  • $$0.2 N, 0.2 N$$
A body of mass $$m$$ is situated at distance $$4R_e$$ above the earth's surface, where $$R_e$$ is the radius of earth how much minimum energy be given to the body so that it may escape
  • $$mgR_e$$
  • $$2mgR_e$$
  • $$\dfrac {mgR_e} {5}$$
  • $$\dfrac {mgR_e} {16}$$
Read the assertion and reason carefully to mark the correct option out of the options given below :

Assertion : Radius of circular orbit of a satellite is made two times, then it areal velocity will also become two times.
Reason : Areal velocity is given as $$\dfrac {dA}{dt}=\dfrac {L}{2m}=\dfrac {mvr}{2m}$$
  • 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
A space shuttle is launched in a circular orbit near the earth's surface. The additional velocity be given to the space - shuttle to get free from the influence of gravitational force, will be.
  • $$1.52\ km/s$$
  • $$2.75\ km/s$$
  • $$3.28\ km/s$$
  • $$5.18\ km/s$$
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 $$d$$ below it. When both $$d$$ and $$h$$ are much smaller than the radius of earth, then
  • $$d = h$$
  • $$d = 2h$$
  • $$d = h/2$$
  • $$d = h$$$$^2$$
The escape velocity for a planet is $$\displaystyle v_{e}$$ A particle starts from rest at a large distance from the planet reaches the planet only under gravitational attraction and passes through a smooth tunnel through its centre Its speed at the centre of the planet will be
  • $$\displaystyle \sqrt{1.5}v_{e}$$
  • $$\displaystyle \frac{v_{e}}{\sqrt{2}}$$
  • $$\displaystyle v_{e}$$
  • zero
The ratio of the radii of the planets $${P}_{1}$$ and $${P}_{2}$$ is $$k$$. The ratio of gravitational field intensity at their surface is $$r$$ then the ratio of the escape velocities from them will be -
  • $$kr$$
  • $$\sqrt{kr}$$
  • $$\displaystyle\sqrt{\frac{k}{r}}$$
  • $$\displaystyle\sqrt{\frac{r}{k}}$$
The dependence of acceleration due to gravity $$g$$ on the distance $$r $$ from the centre of the earth, assumed to be a sphere of radius $$R$$ of uniform density is as shown in figures below. The correct figure is
If $$A$$ is the areal velocity of planet of mass $$M$$. its angular momentum is
  • $$M$$
  • $$2MA$$
  • $$A^2M$$
  • $$AM^2$$
The velocity of a planet revolving around the sun at three different times of a year is shown in the figure. Which among the following alternatives is correct ?
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  • $$v_2\, =\, \displaystyle \frac{v_1\, +\, v_3}{2}$$
  • $$v_1\, =\, \displaystyle \frac{v_2\, +\, v_3}{2}$$
  • $$v_1\, >\, v_2\, >\, v_3$$
  • $$v_1\, <\, v_2\, <\, v_3$$
The variation of $$g$$ with height or depth ($$r$$) is shown correctly by the graph in figure (where $$R$$ is radius of the earth).
Above the earth's surface, the variation of g w.r.t. the height (r) is correctly represented by which of the given proportionalities
  • $$g \propto \dfrac {1}{r^2}$$
  • $$g \propto r$$
  • $$g \propto \ r^2$$
  • $$g \propto r^o$$
The SI unit of G is.
  • $$N^2m^2/kg$$
  • $$Nm^2/kg$$
  • $$N \ ml \ kg$$
  • $$Nm^2/kg^2$$
Where will 'g' be greatest when one goes from the centre of earth to an altitude equal to the radius of the earth?
  • at the surface of earth
  • at the centre of earth
  • at the highest point
  • none of the above
The weight of an object would be minimum when it is placed :
  • At the North Pole
  • At the South Pole
  • At the Equator
  • At the Centre of the Earth
In the motion of the planets, 
  • The angular velocity is constant
  • The linear momentum is constant
  • The angular momentum is constant
  • None of the above
If a body is sent with a velocity of ............... km $$\displaystyle { sec }^{ -1 }$$, it would leave the earth forever. 
  • $$11.9$$
  • $$11.6$$
  • $$11.4$$
  • $$11.2$$
From the centre of the earth to the surface of the earth, the relation between the value of g and distance (r) represented as a proportionality, is given by
  • $$g \propto \dfrac {1}{r^2}$$
  • $$g \propto r$$
  • $$g \propto r^2$$
  • $$g \propto r^o$$
The maximum weight of a body on earth is
  • at the centre of the earth
  • inside the earth
  • on the surface of the earth
  • above the surface of the earth
The value of $$g $$
  • Increases with increase in depth
  • Decreases with increase in depth
  • Remains same regardless of the depth
  • Depends upon the mass of the object
An object is dropped at the surface of the earth from the height of $$3600$$ km. Calculate the ratio of the weight of the body at that height and on the surface of the earth.
  • $$1.34$$
  • $$2.44$$
  • $$6.25$$
  • $$12.32$$
The variation of g with height or depth (r) is shown correctly by the graph in the figure (where R $$=$$ radius of the earth ), 
SI unit of G is $$Nm^{ 2 }{ kg }^{ -2 }$$. Which of the following can also be used as the SI unit of G?
  • $$ m^{ 3 }{ kg }^{ -1 }{ s }^{ -2 }$$
  • $$ m^{ 2 }{ kg }^{ -2 }{ s }^{ -1 }$$
  • $$ m { kg }^{ -3 }{ s }^{ -1 }$$
  • $$ m^{ 2 }{ kg }^{ -3 }{ s }^{ -2 }$$
Where will g be greatest when one goes from the centre of earth to an altitude equal to radius of earth?
  • at the surface of earth
  • at the centre of earth
  • at the highest point
  • none of the above
Maximum weight of the body is
  • at the centre of the eath
  • inside the earth
  • on the surface of the earth
  • above the the surface of the earth
If R is the radius of the earth and g is the acceleration due to gravity on the earth's surface, then mean density of the earth is
  • $$\dfrac { 4\pi G }{ 3gR } $$
  • $$\dfrac { 3\pi R }{ 4gG } $$
  • $$\dfrac { 3 G}{ 4\pi RG } $$
  • $$\dfrac { pi g }{ 12RG } $$
What will be acceleration due to gravity on the surface of moon if its radius is $$\frac { 1 }{ 4 } $$th the radius of the earth and its mass is $$\frac { 1 }{ 80 }$$th the mass of the earth?  
  • $$\frac { g }{ 2 } $$
  • $$\frac { g }{ 3 } $$
  • $$\frac { g }{ 7 } $$
  • $$\frac { g }{ 5 } $$
SI unit of G is.
  • $$N^2 -m^2/kg$$
  • $$N -m^2/kg$$
  • $$N -m/kg$$
  • $$N -m^2/kg^2$$
At what height, is the value of $$g$$ half that on the surface of earth? ($$R =$$ radius of the earth) 
  • $$0.414\ R$$
  • $$R$$
  • $$2\ R$$
  • $$3.5\ R$$
The value of g near the earth's surface is.
  • $$8.9\ ms^{-2}$$
  • $$8.9\ ms^{-1}$$
  • $$9.8\ ms^{-2}$$
  • $$9.8\ ms^{-1}$$
A body of mass $$m$$ is raised to a height $$10R$$ from the surface of the earth, where $$R$$ is the radius of the earth. The increase in potential energy is ($$G =$$ universal constant of gravitation, $$M =$$ mass of the earth and $$g =$$ acceleration due to gravity)
  • $$\dfrac{GMm}{11R}$$
  • $$\dfrac{GMm}{10R}$$
  • $$\dfrac{mgR}{11G}$$
  • $$\dfrac{10GMm}{11R}$$
Let $$g_h$$ and $$g_d$$ be the acceleration due to gravity at height h above the earth's surface and at depth d below the earth's surface respectively. If $$g_h=g_d$$, then the relation between h and d is 
  • $$d = h$$
  • $$d = \dfrac{h}{2}$$
  • $$d = \dfrac{h}{4}$$
  • $$d = 2h$$
The velocity with which a projectile must be fired so that it escapes earth's gravitation does not depend on
  • Mass of the earth
  • Mass of the projectile
  • Radius of the projectile's orbit
  • Gravitational constant
The magnitude of acceleration due to gravity at an altitude 'h' from the earth is equal to its magnitude at a depth 'd'. Find the relation between 'h'and 'd'. If the 'h'and 'd' both increases by $$50$$ %, are the magnitudes of acceleration due to gravity at the new altitude and the new depth equal. 
  • $$d \ =\  h$$
  • $$d\ =\ 2h$$
  • $$\displaystyle h = \frac { d }{ 3 } $$
  • $$d\  =\  4h$$
A body of mass '$$m$$' is raised to a height '$$10R$$' from the surface of the Earth, where '$$R$$' is the radius of the Earth. The increase in potential energy is ____ . ($$G$$ = universal constant of gravitation, $$M$$ = mass of earth and $$g$$ = acceleration due to gravity).
  • $$\displaystyle\frac{GMm}{11R}$$
  • $$\displaystyle\frac{GMm}{10R}$$
  • $$\displaystyle\frac{mgR}{11G}$$
  • $$\displaystyle\frac{10GMm}{11R}$$
The height at which the acceleration due to gravity is $$25\%$$ of that of the surface of earth is ____________. (R=Radius of the earth)
  • $$h=3R$$
  • $$h=2R$$
  • $$h=R$$
  • $$h=\displaystyle\frac{R}{2}$$
The change in the gravitational potential energy when a body of mass m is raised to a height $$nR$$ above the surface of the Earth is (Here R is the radius of the earth)
  • $$\begin{pmatrix}\dfrac{n}{n+1}\end{pmatrix}mgR$$
  • $$\begin{pmatrix}\dfrac{n}{n-1}\end{pmatrix}mgR$$
  • $$nmgR$$
  • $$\dfrac{mgR}{n}$$
If $$g$$ is the acceleration due to gravity on the surface of the earth, the gain in potential energy of an object of mass $$m$$ raised from the earth's surface to a height equal to the radius $$R$$ of the earth is
  • $$\cfrac{mgR}{4}$$
  • $$\cfrac{mgR}{2}$$
  • $$mgR$$
  • $$2mgR$$
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
  • $$3 mg R$$
  • $$\dfrac {1}{3} mg R$$
  • $$2 mg R$$
  • $$\dfrac {2}{3} mg R$$
A body is taken to a height of $$nR$$ from the surface of the earth. The ratio of the acceleration due to gravity on the surface to that at the altitude is
  • $$(n\, +\, 1)^2$$
  • $$(n\, +\, 1)^{-2}$$
  • $$(n\, +\, 1)^{-1}$$
  • $$(n\, +\, 1)$$
If $$g$$ is the acceleration due to gravity on the earth's surface, the gain of 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 will be :
  • $$2mgR$$
  • $$mgR$$
  • $$\dfrac{1}{2}mgR$$
  • $$\dfrac{1}{4}mgR$$
Calculate angular velocity of earth so that acceleration due to gravity at $$60^o$$ latitude becomes zero. (Radius of earth $$=6400$$km, gravitational acceleration at poles$$=10m{/s^2}, \cos 60^o=0.5$$)
  • $$7.8\times 10^{-2}rad/s$$
  • $$0.5\times 10^{-3}rad/s$$
  • $$1\times 10^{-3}rad/s$$
  • $$2.5\times 10^{-3}rad/s$$
Assuming $${ g }_{ \left( moon \right)  }=\left( \dfrac { 1 }{ 6 }  \right) { g }_{ earth }$$ and $${ D }_{ \left( moon \right)  }=\left( \dfrac { 1 }{ 4 }  \right) { D }_{ earth }$$ where $$g$$ and $$D$$ are the acceleration due to gravity and diameter respectively, the escape velocity from the moon is:
  • $$\dfrac { 11.2 }{ 24 }\  { kms }^{ -1 }$$
  • $$11.2\times \sqrt { 24 } \ { kms }^{ -1 }$$
  • $$\dfrac { 11.2 }{ \sqrt { 24 } }\  { kms }^{ -1 }$$
  • $$11.2\times 24\ { kms }^{ -1 }$$
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