IISER 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 angular velocity of a geo-stationary satellite is
- (a)
\(\frac { \pi }{ 12 } deg\quad { h }^{ -1 }\)
- (b)
\(\frac { \pi }{ 6 } deg\quad { h }^{ -1 }\)
- (c)
15 deg h-1
- (d)
15 rad h-1
the value of the gravitational constant (G)
- (a)
depends on the nature of masses
- (b)
depends on the location of masses in the universe
- (c)
is a constant when earth and any other body in the universe are involved
- (d)
none of the above
two identical objects of mass M are initially separated by a very distance. if each object is released from rest and allowed to gravitate toward the other when the sepration of the particles is R, their relative velocity is
- (a)
\(\sqrt { \frac { GM }{ R } } \)
- (b)
\(\sqrt { \frac { 2GM }{ R } } \)
- (c)
\(\sqrt [ 2 ]{ \frac { GM }{ R } } \)
- (d)
\(\frac { 1 }{ 2 } \sqrt { \frac { GM }{ R } } \)
a shaft drilled through the earth along its diameter. if a particle is projected upward from the centre of the earth the velocuty that permits the particle to escape from the earth is
- (a)
17.3 km s-1
- (b)
13.7 km s-1
- (c)
11.2 km s-1
- (d)
2.4 km s-1
a simple pendulum has a time period T1 when on the earth's surface , and T2 when taken to a height R above the earth surface , where R is radius of the earth . the value of T2 / T1 IS
- (a)
1
- (b)
\(\sqrt { 2 } \)
- (c)
4
- (d)
2
at what height above the earths surface the value of g is same as that in a mine 10km deep
- (a)
10 km
- (b)
20km
- (c)
5 km
- (d)
15 km
if the satellite is stopped suddenly in its orbit and is allowed to falll freely into the earths surface with what speed it hits the surface of the earth?
- (a)
7.92 km s-1
- (b)
11.2 km s-1
- (c)
8.92 km s-1
- (d)
5.6 km s-1
The value of escape velocity at the earth's surface is 11km/s. a planet has a radius twice that of the earth. The value of escape velocity at this planet is
- (a)
11 km/s
- (b)
28 km/s
- (c)
32 km/s
- (d)
22 km/s
The time period of a satellite of the earth is 5h. If the separation between the earth and the satellite is increased to 4times the previous value, then the new time period will become
- (a)
10h
- (b)
80h
- (c)
40h
- (d)
20h
The time period of an earth satellite in circular orbit is independent of:
- (a)
the mass of the satellite
- (b)
radius of its orbit
- (c)
both the mass of satellite and radius of the orbit
- (d)
neither the mass of satellite nor the radius of its orbit
The escape velocity of a body from the earth is u.What is the escape velocity from a planet whose mass and radius are twice those of the earth?
- (a)
2u
- (b)
u
- (c)
4u
- (d)
16u
Gravitational force between two point masses m and M separated by a distance is F. Now if a point mass 2m is placed next to m in contact with it, the force on M due to m and the total force on M are:
- (a)
2F,F
- (b)
F,2F
- (c)
F,3F
- (d)
F,F
If a person with a spring balance and a body hanging from it goes up and up in an aeroplane, then the reading of the weight of the body as indicated by the spring balance will:
- (a)
go on increasing
- (b)
go on decreasing
- (c)
first increase and then decrease
- (d)
remain the same
The masses and radii of the earth and the moon are M1 R1 and M2 , R2 respectively. Their centres are at distance d apart. The minimum speed with which a particle of mass m should be projected from a point midway the two centres so as to escape to infinity is:
- (a)
\(\sqrt { \frac { 2G({ M }_{ 1 }+{ M }_{ 2 }) }{ d } } \)
- (b)
\(\sqrt { \frac { 4G({ M }_{ 1 }+{ M }_{ 2 }) }{ d } } \)
- (c)
\(\sqrt { \frac { 4G M _{ 1 }+{ M }_{ 2 }}{ d } } \)
- (d)
\(\sqrt { \frac { G({ M }_{ 1 }+{ M }_{ 2 }) }{ d } } \)
In a certain region of space, the gravitational field is given by -k/r, where r is the distance and k is a constant. If the gravitational potential at r = r0 be V0, then what is the expression for the gravitational potential (V)?
- (a)
k log (r/r0)
- (b)
k log (r0 / r)
- (c)
V0 + k log (r/r0)
- (d)
V0 + k log (r0/r)
The gravitational potential due to the earth at infinite distance from it is zero. Let the gravitational potential at a point P be -5 J/kg . Suppose, we arbitrarily assume the gravitational potential at infinity to be + 10 J/kg, then the gravitational potential at P will be:
- (a)
-5 J/kg
- (b)
+ 5 J/kg
- (c)
-15 J/kg
- (d)
+ 15 J/kg
The metallic bob of a simple pendulum has the relative density S. The time period of this pendulum is T. If the metallic bob is immersed in water, then the new time period is given by:
- (a)
\(T\left( \frac { \rho -1 }{ \rho } \right) \)
- (b)
\(\frac { \rho }{ (\rho -1) } T\)
- (c)
\(T\sqrt { \left( \frac { \rho -1 }{ \rho } \right) } \)
- (d)
\(T\sqrt { \frac { \rho }{ (\rho -1) } } \)
You are given 32 identical balls all of equal weight except I which is heavier than the others. You are given a beam balance but no weight box. What is the minimum number of weighings required to identify the balls of different weight?
- (a)
3
- (b)
4
- (c)
5
- (d)
6
A space ship moves from the earth to the moon and back. The greatest energy required for the space ship is to overcome the difficulty in:
- (a)
entering the earth's gravitational field
- (b)
take-off from the earth's field
- (c)
take-off from lunar surface
- (d)
entering the moon's lunar surface
A body is orbiting very close to the earth's surface with kinetic energy KE. The energy required to completely escape from it is:
- (a)
\(\sqrt{2}\)KE
- (b)
KE
- (c)
KE/\(\sqrt{2}\)
- (d)
none of these
The acceleration of a body due to the attraction of the earth (radius R) at a distance 2R from the surface of the earth is: (g = acceleration due to gravity at the surface ofthe earth)
- (a)
g/9
- (b)
g/3
- (c)
g/4
- (d)
g
The mean radius of the earth is R, its angular speed about its own axis is \(\omega\) and the acceleration due to gravity at the earth's surface is g. The cube of the radius of orbit of geostationary satellite will be:
- (a)
(R2g/\(\omega\))
- (b)
(R2\(\omega\)/g)
- (c)
(Rh/\(\omega ^{2}\))
- (d)
(R2g/\(\omega ^{2}\))
The mass of a planet is six times that ofthe earth. The radius of the planet is twice that of the earth. If the escape velocity from the earth is v, then the escape velocity from the planet is:
- (a)
\(\sqrt { 3 } \upsilon \)
- (b)
\(\sqrt { 2 } \upsilon \)
- (c)
\(\upsilon\)
- (d)
\(\sqrt { 5 } \upsilon \)
Two satellites of the earth, S1 and S2 are moving in the same orbit. The mass of S1 is four times the mass of S2. Which one of the following statements is true?
- (a)
The potential energies of the earth and satellite in the two cases are equal.
- (b)
S1 and S2 are moving with the same speed.
- (c)
The kinetic energies of the two satellites are equal.
- (d)
The time period of S1 is four times that of S2.
The length of the second's pendulum is decreased by 0.3 em when it is shifted to Chennai from London. If the acceleration due to gravity at London is 981 cm/s2, the acceleration due to gravity at Chennai is: (Assume \(\pi^{2}\)= 10)
- (a)
981 cm/s2
- (b)
978 cm/s2
- (c)
984 cm/s2
- (d)
975 cm/s2
A body is projected up from the surface of the earth with a velocity equal to \(\frac{3}{4}\)th of its escape velocity. If R be the radius of the earth, the height it reaches is:
- (a)
\(\frac{3R}{10}\)
- (b)
\(\frac{9R}{7}\)
- (c)
\(\frac{8R}{5}\)
- (d)
\(\frac{9R}{5}\)
If the earth were to cease rotating about its own axis. The increase in the value of g in C.G.S. system at a place of latitude of 450 will be:
- (a)
2.68
- (b)
1.68
- (c)
3.36
- (d)
0.34
If the earth is one-fourth of its present distance from the sun, the duration of the year will be changed to :
- (a)
\(\frac{1}{4}\)th of the present year
- (b)
\(\frac{1}{8}\)th of the present year
- (c)
\(\frac{7}{8}\)th of the present year
- (d)
\(\frac{1}{16}\)th of the present year
A period of geostationary satellite is :
- (a)
30h
- (b)
24h
- (c)
48h
- (d)
12h