CBSE Questions for Class 11 Engineering Physics Gravitation Quiz 5 - MCQExams.com

An object lying at the equator of the earth will fly off the surface (will feel weightlessness), if the length of the day becomes
  • $$1.00 h$$
  • $$1.41 h$$
  • $$17.0 h$$
  • $$17.0 min$$
In a relation $$\displaystyle \sqrt{\frac{2GM}{R}} \geq C$$, G stands for universal gravitational constant, M for mass of a very very dense material, R for a small radius and C for velocity of light. Then,
  • the above relation indicates that orbital velocity is equal to velocity of light.
  • the above relation indicates something like a black hole.
  • the above relation indicates that the light is escaping.
  • the above relation indicates that any object starting from the given mass with speed more than light will return to it.
If $${ g }$$ is the acceleration due to gravity on the earth's surface, the change 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
  • $$\displaystyle \dfrac { mgR }{ 2 } $$
  • $$\displaystyle { 2mgR }$$
  • $$\displaystyle { mgR }$$
  • $$\displaystyle { -mgR }$$
Two equals masses each $$m$$ and $$m$$ are hung from a balance whose scale pans differ in vertical height by $$'h'$$. The error in weighing in terms of density of the earth $$\rho $$ is:
  • $$\displaystyle \pi G \rho m h$$
  • $$\cfrac { 1 }{ 3 } \pi G \rho m h$$
  • $$\cfrac { 8 }{ 3 } \pi G \rho m h$$
  • $$\cfrac { 4 }{ 3 } \pi G \rho m h$$
A spring balance is calibrated at sea level. If this balance is used to measure the weight of a body at successive increasing heights from the surface of the earth, then the weight indicated by spring balance will
  • decrease continuously
  • increase continuously
  • first decrease, then increase
  • remains constant
A small mass $$m$$ is moved slowly from the surface of the earth to a height $$h$$ above the surface. The work done (by an external agent) in doing this is
  • $$mgh$$, for all values of $$h$$
  • $$mgh$$, for $$h<< R$$
  • $$1/2mgR$$, for $$h=R$$
  • $$-1/2mgR$$, for $$h=R$$
If both the mass and radius of the earth decrease by $$1$$% the value of
  • acceleration due to gravity would decrease by nearly $$1$$%
  • acceleration due to gravity would increase by $$1$$%
  • escape velocity from the earth's surface would decrease by $$1$$%
  • the gravitational potential energy of a body on earth's surface will remain unchanged
A body of mass $${ m }$$ rises to a height $${ h }=\dfrac{R}{5}$$ from the earth's surface where $${ R }$$ is the earth's radius. If  $$g$$ is acceleration duem to gravity at the earth's surface, the increase in potential energy is
  • $${ mgh }$$
  • $$\cfrac { 4 }{ 5 } { mgh }$$
  • $$\cfrac { 5 }{ 6 } { mgh }$$
  • $$\cfrac { 6 }{ 7 } { mgh }$$
The value of $${ g }$$ at a certain height $${ h }$$ above the free surface of the earth is $${ x }/{ 4 }$$ where $${ x }$$ is the value of $${ g }$$ at the surface of the earth. The height $${ h }$$ is
  • $${ R }$$
  • $${ 2R }$$
  • $${ 3R }$$
  • $${ 4R }$$
The change in the value of $$g$$ at a height $$h$$ above the surface of earth is the same as at a depth $$d$$ below the earth. When both $$d$$ and $$h$$ are much smaller than the radius of earth, then which one of the following is correct?
  • $$d=\cfrac { h }{ 2 } $$
  • $$d=\cfrac { 3h }{ 2 } $$
  • $$d=2h$$
  • $$d=h$$
If an artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of the escape velocity from the earth, the height of the satellite above the surface of the earth is
  • $$2R$$
  • $$\cfrac {R}{2}$$
  • $$R$$
  • $$\cfrac{R}{4}$$
An object is taken from a point $$P$$ to another point $$Q$$ in a gravitational field:
  • assuming the earth to be spherical, if both $$P$$ and $$Q$$ lie on the earth's surface, the work done is zero
  • if $$P$$ is on the earth's surface and $$Q$$ above it, the work done is minimum when it is taken along the straight line $$PQ$$
  • the work done depends only on the position of $$P$$ and $$Q$$ and is independent of the path along which the particle is taken
  • there is no work done if the object is taken from $$P$$ to $$Q$$ and then brought back to $$P$$ along any path
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 earth to a height equal to the radius $$R$$ of the earth is
  • $$\cfrac { 1 }{ 2 } { mgR }$$
  • $${ 2mgR }$$
  • $${ mgR }$$
  • $$\cfrac { 1 }{ 4 } { mgR }$$
The gravitational potential due to earth at infinite distance from it is zero. Let the gravitational potential at a point $$P$$ be $$-{ 5 }{ J }{ kg }^{ -1 }$$. Suppose, we arbitrarily assume the gravitational potential at infinity to be $$+{ 10 }{ J }{ kg }^{ -1 }$$, then the gravitational potential at $$P$$ will be
  • $$-{ 5 }{ J }{ kg }^{ -1 }$$
  • $$+{ 5 }{ J }{ kg }^{ -1 }$$
  • $$-{ 15 }{ J }{ kg }^{ -1 }$$
  • $$+{ 15 }{ J }{ kg }^{ -1 }$$
A man weighs $$80 kg$$ on the surface of earth of radius $$R$$. At what height above the surface of earth his weight will be $$40 kg$$?
  • $$\dfrac { R }{ 2 } $$
  • $$\sqrt { 2 } { R }$$
  • $$\left( \sqrt { 2 } -{ 1 } \right) { R }$$
  • $$\left( \sqrt { 2 } +{ 1 } \right) { R }$$
Let $$V$$ and $$E$$ denote the gravitational potential and gravitational field at a point. It is possible to have
  • $$\displaystyle V=0$$ and $$E=0$$
  • $$\displaystyle V=0$$ and $$E \neq 0$$
  • $$\displaystyle V\neq 0$$ and $$E = 0$$
  • All of the above
Which of the following are not correct?
  • The escape velocity for the Moon is $$6km$$ $${s}^{-1}$$
  • The escape velocity from the surface of Moon is $$v$$. The orbital velocity for a satellite to orbit very close to the surface of Moon is $$v/2$$
  • When an earth satellite is moved from one stable orbit to a further stable orbit, the gravitational potential energy increases
  • The orbital velocity of a satellite revolving in a circular path close to the planet is independent of the density of the planet.
The escape velocity of a projectile from the earth is approximately
  • $$\displaystyle 7$$ $$km/sec$$
  • $$\displaystyle 112$$ $$km/sec$$
  • $$\displaystyle 11.2$$ $$km/sec$$
  • $$\displaystyle 1.1$$ $$km/sec$$
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
  • $$\cfrac { 1 }{ 2 } mgR$$
  • $$2mgR$$
  • $$\cfrac { 1 }{ 4 } mgR$$
  • $$mgR$$
There is no atmosphere on the moon because.
  • It is closer to the earth
  • It revolves round the earth
  • It gets light from the sun
  • The escape velocity of gas molecules is lesser than their root mean square velocity
The escape velocity of an object projected from the surface of a given planet is independent of
  • Radius of the planet
  • The direction of projection
  • The mass of the planet
  • None of these
The weight of a body at the centre of the earth is
  • Zero
  • Infinite
  • Same as on the surface on earth
  • None of these
If $$v_e$$ and $$v_0$$ represent the escape velocity and orbital velocity of a satellite corresponding to circular orbit of radius $$R$$, then
  • $$\displaystyle v_e=v_o$$
  • $$\displaystyle v_e=\sqrt 2 v_o$$
  • $$\displaystyle v_e=(1/\sqrt {2})v_o$$
  • $$\displaystyle v_e$$ and $$\displaystyle v_0$$ are not related
Taking the gravitational potential at a point infinte distance away as zero, the gravitational potential at a point $$A$$ is $$-5$$ unit. If the gravitational potential at a point infinite distance away is taken as $$+10$$ units, the potential at a point $$A$$ is
  • $$\displaystyle -5$$ unit
  • $$\displaystyle +5$$ unit
  • $$\displaystyle +10$$ unit
  • $$\displaystyle +15$$ unit
The mass of the moon is $$1/81$$ of earth's mass and its radius $$1/4$$ that of the earth. If the escape velocity from the earth's surface is $$11.2$$ km/sec. its value from the surface of the moon will be
  • $$\displaystyle 0.14 kms^{-1}$$
  • $$\displaystyle 0.5 kms^{-1}$$
  • $$\displaystyle 2.5 kms^{-1}$$
  • $$\displaystyle 5.0 kms^{-1}$$
The kinetic energy needed to project a body of mass $$m$$ from the earth surface (radius $$R$$) to infinity is
  • $$\displaystyle mgR/2$$
  • $$\displaystyle 2mgR$$
  • $$\displaystyle mgR$$
  • $$\displaystyle mgR/4$$
The ratio of the radii of the planets $$R_1$$ and $$R_2$$ is $$k$$. The ratio of the acceleration due to gravity is $$r$$. The ratio of the escape velocities from them will be
  • $$\displaystyle kr$$
  • $$\displaystyle \sqrt {kr}$$
  • $$\displaystyle \sqrt {(k/r)}$$
  • $$\displaystyle \sqrt {(r/k)}$$
The radius of a planet is $$1/4^{th}$$ of $$R_e$$ and its acc, due to gravity is $$2g$$. What would be the value of escape velocity on the planet, if escape velocity on earth is $$v_e$$
  • $$\displaystyle \frac {v_e}{\sqrt {2}}$$
  • $$\displaystyle v_e \sqrt {2}$$
  • $$\displaystyle 2v_e$$
  • $$\displaystyle \frac {v_e}{2}$$
The gravitational potential difference between the surface of a planet and a point $$20 m$$ above the surface is $$2$$ joule/kgs. If the gravitational field is uniform, then the work done in carrying a $$5$$ kg body to a height of $$4 m$$ above the surface is
  • $$\displaystyle 2 J$$
  • $$\displaystyle 20 J$$
  • $$\displaystyle 40 J$$
  • $$\displaystyle 10 J$$
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 by $$B$$ goes on increasing
  • $$B$$ goes on decreasing and that by $$A$$ goes on increasing
  • Each decreases at the same rate
  • Each decreases at different
The weight of an object in the coal mine, sea level and at the top of the mountain, are respectively $$W_1$$, $$W_2$$ and $$W_3$$ then
  • $$\displaystyle W_1 < W_2 > W_3$$
  • $$\displaystyle W_1 = W_2 = W_3$$
  • $$\displaystyle W_1 < W_2 < W_3$$
  • $$\displaystyle W_1 > W_2 > W_3$$
The escape velocity of a body depends upon its mass as
  • $$\displaystyle m^0$$
  • $$\displaystyle m^1$$
  • $$\displaystyle m^2$$
  • $$\displaystyle m^3$$
The largest and the shortest distance of the earth from the sun is $$r_1$$ and $$r_2$$. Its distance from the sun when it is at perpendicular to the major axis of the orbit drawn from the sun:
  • $$\displaystyle (r_1+r_2)/4$$
  • $$\displaystyle (r_1+r_2)/(r_1-r_2)$$
  • $$\displaystyle 2r_1r_2/(r_1+r_2)$$
  • $$\displaystyle (r_1+r_2)/3$$
Escape velocity when a body of mass $$m$$ is thrown vertically from the surface of the earth is $$v$$, what will be the escape velocity of another body of mass $$4 m$$ if thrown vertically
  • $$\displaystyle v$$
  • $$\displaystyle 2v$$
  • $$\displaystyle 4v$$
  • None of these
The total mechanical energy E possessed by a body of mass 'm',  moving with a velocity 'v' at a height 'h' is given by : $$E\, =\, \displaystyle \frac{1}{2}\, mv^{2}\, +\, mgh.$$ Make 'm' the subject of formula.
  • $$m\, =\, \displaystyle \frac{2E}{v^{2}\, +\, gh}$$
  • $$m\, =\, \displaystyle \frac{2E}{v^{2}\, +\, 2gh}$$
  • $$m\, =\, \displaystyle \frac{3E}{v^{2}\, +\, 2gh}$$
  • $$m\, =\, \displaystyle \frac{E}{v^{2}\, +\, 2gh}$$
A spherical uniform planet is rotating about its axis. The velocity of a point on its equator is $$V$$. Due to the rotation of a planet about its axis the acceleration due to gravity $$g$$ at equator is $$\dfrac{1}{2}$$ of $$g$$ at poles. The escape velocity of a particle on the pole of a planet in terms of $$V$$ is
  • $$\displaystyle V_e=2V$$
  • $$\displaystyle V_e=V$$
  • $$\displaystyle V_e=\dfrac{V}{2}$$
  • $$\displaystyle V_e=\sqrt {3}V$$
A satellite of mass '$$m$$', moving around the earth in a circular orbit of radius $$R$$, has angular momentum $$L$$. The areal velocity of satellite is :
  • $$\displaystyle L/2m$$
  • $$\displaystyle L/m$$
  • $$\displaystyle 2L/m$$
  • $$\displaystyle 2L/m_e$$
In the region of only gravitational fields of mass '$$M$$' a particle is shifted from $$A$$ to $$B$$ via three different paths of length 5m, 10m and 25m. The work done in different paths is $$W_1, W_2, W_3$$ respectively then:
  • $$\displaystyle W_1=W_2=W_3$$
  • $$\displaystyle W_1>W_2>W_3$$
  • $$\displaystyle W_1=W_2>W_3$$
  • $$\displaystyle W_1 < W_2 < W_3$$
The amount of work done in lifting a mass '$$m$$' from the surface of the earth to height $$2R$$ is
  • $$\displaystyle 2mgR$$
  • $$\displaystyle 3mgR$$
  • $$\displaystyle \frac {3}{2}mgR$$
  • $$\displaystyle \frac {2}{3}mgR$$
At what height from the surface of earth will the value of g be reduced by $$36$$% from the value at the surface? $$R = 6400km$$.
  • $$400 km$$
  • $$800 km$$
  • $$1600 km$$
  • $$3200 km$$
The change in potential energy, when a body of mass $$m$$ is raised to a height $$nR$$ from the earth's surface is $$(R=$$ radius of earth$$)$$
  • $$\displaystyle mgR \left ( \frac {n}{n-1}\right )$$
  • $$\displaystyle nmgR$$
  • $$\displaystyle mgR \left ( \frac {n^2}{n^2+1}\right )$$
  • $$\displaystyle mgR \left ( \frac {n}{n+1}\right )$$
The escape velocity from a planet is $$v_e$$. A tunnel is dug along a diameter of the planet and a small body is dropped into it at the surface. When the body reaches the centre of the planet, its speed will be
  • $$\dfrac {u}{\sqrt {2}}$$
  • $$u$$
  • $$\dfrac {u}{2\sqrt {2}}$$
  • $$\dfrac {u}{{2}}$$
Weight of a body of mass $$m$$ decreases by $$1%$$ when it is raised to height h above the earth's surface. If the body is taken to a depth $$h$$ in a mine, then in its weight will
  • decrease by $$0.5%$$
  • decrease by $$2%$$
  • increase by $$0.5%$$
  • increase by $$1%$$
A missile is lauched with a velocity less than the escape velocity. Sum of its kinetic energy and potential energy is.
  • positive
  • negative
  • may be negative or positive depending upon its

    initial velocity
  • zero
Which of the following statement is wrong for acceleration due to gravity.
  • $$g$$ decreases on going above the surface of earth
  • $$g$$ increases on going below the surface of earth
  • $$g$$ is maximum at pole
  • $$g$$ increases on going from equator to poles
The value of '$$g$$' reduces to half of its value at surface of earth at a height '$$h$$', then
  • $$h = R$$
  • $$h = 2R$$
  • $$h \equiv ( \sqrt 2 +1)R$$
  • $$h \equiv ( \sqrt 2 -1)R$$
If $$v_{e}$$ is the escape velocity for earth when a projectile is fired from the surface of earth. Then the escape velocity if the same projectile is fired from its centre is
  • $$\displaystyle \sqrt{\frac{3}{2}}v_{e}$$
  • $$\displaystyle \frac{3}{2}v_{e}$$
  • $$\displaystyle \sqrt{\frac{2}{3}}v_{e}$$
  • $$\displaystyle \frac{2}{3}v_{e}$$
The gravitational potential energy of a body at a distance $$r$$ from the centre of earth is $$U$$. Its weight at a distance $$2r$$ from the centre of earth is
  • $$\displaystyle\frac{U}{r}$$
  • $$\displaystyle\frac{U}{2r}$$
  • $$\displaystyle\frac{U}{4r}$$
  • $$\displaystyle\frac{U}{\sqrt{2}r}$$
If the radius of moon is $$1.7 \times 10^{6}\  m$$ and its mass is $$7.34\times 10^{22}\  kg$$. Then its escape velocity is
  • $$2.4\times 10^{3}\ ms^{-1}$$
  • $$2.4\times 10^{2}\ ms^{-1}$$
  • $$3.4\times 10^{3}\ ms^{-1}$$
  • $$3.4\times 10^{2}\ ms^{-1}$$
Acceleration due to gravity at earth's surface is '$$g$$' m/s$$^2$$. Find the effective value of acceleration due to gravity at a height of $$32 km$$ from sea level :($$R_e = 6400 km$$).
  • $$0.5 g ms^{2}$$
  • $$0.99 g ms^{2}$$
  • $$1.01 g ms^{2}$$
  • $$0.90 g ms^{2}$$
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