Physics - Gravitation
Exam Duration: 45 Mins Total Questions : 30
consider a body at rest on the surface of the rotating earth. if the gravitational force of attraction between the body and the earth vanishes but the earth is still rotating, the body will
- (a)
fly forward along the tangent to the earth's surface
- (b)
fly away outward along the radius of the
- (c)
fly backward along the tangent to the earth's surface
- (d)
move backward a little distance and then remain at rest
the moon completes its one revolution around the earth is 27 days. A satellite encircling the earth in a orbit of radius equal to half of the satellite will complete its ine revolution in nearly
- (a)
\(\frac { 27 }{ { (4) }^{ 1/3 } } \) days and will resolve 2.7 times faster
- (b)
10 days and will resolve 2.7 times faster
- (c)
13.5 days and will resolve 2.7 times faster
- (d)
19 days and will resolve with the same speed
an artificial satellite has rotational kinetic energy K and time period of revolution. T as it nears the end of its life", it is decreasing in altitude.then
- (a)
K and T increase progressively
- (b)
K and T decrease progressively
- (c)
K increase but T increases progressively
- (d)
K decrease but T increases progressively
suppose a shaft is drilled through the earth along a diameter . if aparticle is dropped into the shaft at the earth's surface it will pass through the centre of the earth with a speed of
- (a)
11.2 km s-1
- (b)
7.91 km s-1
- (c)
13.7 km s-1
- (d)
2.4 km s-1
earth is flattened al poles, bulged at the equator. this is due to
- (a)
the angular veloicity of spinning about its axis is less at equator
- (b)
the angular veloicity of spinning about its axis is more at equator
- (c)
the centripetal force is more at the equater than at the poles
- (d)
earth revolves round the sun in an elliptic orbit
the first cosmic velocity from earth is
- (a)
8 km s-1
- (b)
11 km s-1
- (c)
17 km s-1
- (d)
2.9 x 105 km s-1
if the radius of the earth were to shrink by 1% its mass remaining same the acceleration due to gravity on the earths surface would
- (a)
decrease 2%
- (b)
remain unchanged
- (c)
increase 2%
- (d)
become zero
a satellite is moving around the earth with speed \(\vartheta \) in a circular orbit of radius r. if the orbit radius is decreased by1% the speed of the satellite will
- (a)
increase by 1%
- (b)
increase by 0.5%
- (c)
decrease by1%
- (d)
decrease by 0.5%
the escape velocity from the surface of a planet is 10 ms-1 if a mass of 2 kg falls from infinity to the surface of the planet the magnitude pf ptential energy on reachimg the surface will be
- (a)
zero
- (b)
10-8 j
- (c)
0.5x10-8 j
- (d)
10-8 j
A body weighing 18N at the north pole of the earth and in a geostationary satellite at the distance 10R from the earth's centre. Calulate the true weight of the body. (take, radius of the earth=R)
- (a)
0.2N
- (b)
0.4N
- (c)
0.18N
- (d)
0.3N
If mass M is split into two parts m and (M - m) which are then separated by a distance, the ratio of mass\(\frac{m}{M}\) that maximises the gravitational force between the two parts is:
- (a)
1:2
- (b)
1:1
- (c)
2:1
- (d)
1:4
Two concentric shells have masses M and m and their radii are R and r respectively, where R > r. What is the gravitational potential at their common centre?
- (a)
\(-{GM\over R}\)
- (b)
\(-{GM\over r}\)
- (c)
\(-G[{M\over R}-{m\over r}]\)
- (d)
\(-G[{M\over R}+{m\over r}]\)
A rocket is fired vertically from the ground with resultant vertical acceleration of 10 m/sec2 . If the fuel is finished in one minute and it continues to move up, the maximum height reached by it is nearly:
- (a)
40 km
- (b)
20 km
- (c)
10 km
- (d)
80 km
If the radius of the earth's orbit around the sun is R and the time period of revolution of the earth around the sun is T. The mass of the sun is:
- (a)
\(\frac { { GT }^{ 3 } }{ { 4\pi }^{ 2 }{ R }^{ 2 } } \)
- (b)
\(\frac { 4{ \pi }^{ 2 }{ R }^{ 3 } }{ GT^{ 2 } } \)
- (c)
\(\sqrt { \frac { 4\pi ^{ 2 }{ R }^{ 3 } }{ { GT }^{ 2 } } } \)
- (d)
\(\left[ \frac { 4{ \pi }^{ 2 }{ R }^{ 3 } }{ { GT }^{ 2 } } \right] ^{ 1/3 }\)
At the surface of a certain planet acceleration due to gravity is one-quarter of that on the earth. If a brass ball is transported to this planet, then which one of the following statements is not correct?
- (a)
The mass of the brass ball on this planet is a quarter of its mass as measured on the earth.
- (b)
The weight of the brass ball on this planet is a quarter of the weight as measured on the earth.
- (c)
The brass ball has same mass on the other planet as on the earth.
- (d)
The brass ball has the same volume on the other planet as on the earth.
What will be the escape velocity on some planet which is having radius four times that of the earth and gravitational acceleration equal to the earth:
- (a)
equal to escape velocity on the earth
- (b)
one-third of escape velocity on the earth
- (c)
half of escape velocity on the earth
- (d)
two times of escape velocity on the earth
The period of the moon's rotation around the earth is nearly 29 days. If the moon's mass were 2-fold, its present value and all other things remained unchanged, the period of the moon's rotation would be nearly:
- (a)
29\(\sqrt{2}\)days
- (b)
29\(\sqrt{2}\)days
- (c)
29x2 days
- (d)
29 days
By what percentage the energy of a satellite has to be increased to shift it from an orbit of radius r to 3/2 r ?
- (a)
66.7%
- (b)
33.3%
- (c)
75%
- (d)
20.3%
For a satellite moving in an orbit around the earth, the ratio of kinetic energy to potential energy is:
- (a)
1/2
- (b)
1/\(\sqrt{2}\)
- (c)
2
- (d)
\(\sqrt{2}\)
3 particles each of mass m are kept at vertices of an equilateral triangle of side L. The gravitational field at the centre due to these particles is:
- (a)
Zero
- (b)
3GM/L2
- (c)
9 GM/L2
- (d)
12 GM/\(\sqrt{3}\)L2
If a satellite of mass m is revolving around the earth with distance r from centre, then total energy is:
- (a)
-\(\frac{GMm}{r}\)
- (b)
-\(\frac{2GMm}{r}\)
- (c)
-\(\frac{GMm}{2r}\)
- (d)
+\(\frac{GMm}{2r}\)
The distance of saturn and neptune from the sun is nearly 1012 and 1013 m, respectively. Assuming they move in circular orbits, their time periods will be in the ratio:
- (a)
1000: 1
- (b)
1 : 100
- (c)
10: 1
- (d)
1 : 10\(\sqrt{10}\)
A satellite is launched in a circular orbit of radius R around the earth. A second satellite is launched into an orbit of radius 1.01 R. The period of second satellite is longer than the first one (approximately) by:
- (a)
1.5%
- (b)
0.5%
- (c)
3%
- (d)
1%
The orbit of a satellite moving around the earth in the equatorial plane, as viewed from the earth appears to be stationary. What is the radius (approximate) of the orbit?
(Where G is gravitational constant, M is mass of the earth and cois the angular velocity of the earth)
- (a)
(GM/2\(\omega^{2}\))1/3
- (b)
(GM/\(\omega^{2}\))1/3
- (c)
(GM/\(\omega^{2}\))1/2
- (d)
(2GM/\(\omega^{2}\))1/3
A spherically symmetric gravitational system of particles has a mass density \(\rho =\begin{cases} { \rho }_{ 0 } \ for \ r\le R \\ 0 \ for \ r>R \end{cases}\)
where Po is a constant. A test mass can undergo circular motion under the influence of the gravitational field of particles. Its speed u as a function of distance r (0< r< \(\infty \)) from the centre of the system is represented by:
- (a)
- (b)
- (c)
- (d)
The additional kinetic energy to be provided to a satellite of mass m revolving around a planet of mass M, to transfer it from a circular orbit of radius R 1 to another of radius Rz (R2 > R1 ) is
- (a)
GmM\(\left( \frac { 1 }{ { R }_{ 1 }^{ 2 } } -\frac { 1 }{ { R }_{ 2 }^{ 2 } } \right) \)
- (b)
\(\left( \frac { 1 }{ { R }_{ 1 } } -\frac { 1 }{ { R }_{ 2 } } \right) \)
- (c)
2GmM\(\left( \frac { 1 }{ { R }_{ 1 } } -\frac { 1 }{ { R }_{ 2 } } \right) \)
- (d)
GmM\(\left( \frac { 1 }{ { R }_{ 1 } } -\frac { 1 }{ { R }_{ 2 } } \right) \)
A particle of mass m is thrown upwards from the surface of the earth, with a velocity u. The mass and the radius of the earth are, respectively, M and R. G is gravitational constant and g is acceleration due to gravity on the surface of the earth. The minimum value of u so that the particle does not return back to the earth is :
- (a)
\(\sqrt { \frac { 2GM }{ { R }^{ 2 } } } \)
- (b)
\(\sqrt{\frac{2GM}{R}}\)
- (c)
\(\sqrt { \frac { 2gM }{ { R }^{ 2 } } } \)
- (d)
\(\sqrt{2gR^{2}}\)
Pick out the wrong statement from the following:
- (a)
The SI unit of universal gravitational constant is Nm2 kg-2
- (b)
The gravitational force is a conservative force.
- (c)
The force of attraction due to a hollow spherical shell of uniform density on a point mass inside it is zero.
- (d)
The centripetal acceleration of the satellite is equal to acceleration due to gravity.
- (e)
Gravitational potential energy =\(\frac{gravitational \ potential}{mass \ of \ the \ body}\)
A spherical shell is cut into two pieces along a chord as shown in the figure. P is a point on the plane of the chord. The gravitational field at P due to the upper part is I1 and that due to the lower part is I2. What is the relation between them?
- (a)
I1>I2
- (b)
I1<I2
- (c)
I1=I2
- (d)
None of these
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