Physics - Gravitation
Exam Duration: 45 Mins Total Questions : 30
the inertial mass of a body is considered as
- (a)
the mass at rest
- (b)
the mass in motion
- (c)
referred to gravitational pull
- (d)
the concept in effective weight
if g is accelaration due to gravity on the surface of earth
- (a)
the value of the accelaration due to gravity at the surface of the moon is 0.165g
- (b)
the value of the accelaration due to gravity at the surface of the sun is 27.9 g
- (c)
the minimum velocity that an object must have at the surface on the earth if it is to escaoe from the solar system (assumed to consist only of the sun and the earth ) and proceed infinitely far away is 43.6 km s-1
- (d)
all of the above statements are correct
the escsape velocity of a body projected from the surface of the earth vertically upwards is 112 km s-1 if the body is projected in a direction making an angle 300 with the vertical then the new escape velocity will be
- (a)
(11.2/2) km s-1
- (b)
\((11.2\quad x\sqrt { 3 } /2)\quad km\quad { { s }^{ -1 } }\)
- (c)
22.4 km s-1
- (d)
11.2 km s-1
a satellite is launched into ma circular orbits of radius R around the earth . A second satellite is launched into an orbit of radius (1.01) R. the period of the second satellite is larger than that of the first one by approximately
- (a)
0.5%
- (b)
1.0%
- (c)
1.5%
- (d)
3.0%
a seconds pendulum is taken inside 1 km from sea level in one day it
- (a)
loses 13.5 s
- (b)
gains 13.5 s
- (c)
loses 7 s
- (d)
gains 7 s
If one of the satellites of jupiter has an orbital period 1.769 days and the radius of the orbit is 4.22X108 m. The mass of jupiter is about,
- (a)
one thousandth that of the sun
- (b)
one hundredth that of the sum
- (c)
one tenth that of the sun
- (d)
half of that of the sun
A body of mass m is elevated upto a height R/4 from the earth's surface, where, R is the radius of the earth. The potential is incresed by (take, acceleration due to gravity at the earth's surface =g)
- (a)
\(4mgR\over3\)
- (b)
\(mgR\over5\)
- (c)
\(3mgR\over16\)
- (d)
mgR
A planet is revolving around the sun in a circular orbit with a radius r. The time period is T. If the force between the planet and star is proportional to r-3/2, then the square of time period is proportional to
- (a)
r3/2
- (b)
r3
- (c)
r
- (d)
r5/2
Two satellites A and B revolve round the same planet in coplanar circulr orbits lying in the same plane. Their periods of revolutions are 1h and 8h, respectively. The radius of the orbit of A is 104 km. The speed of B is relative to A. When they are closed, in kmh-1 is
- (a)
\(3\pi\times10^4\)
- (b)
zero
- (c)
\(4\pi\times10^4\)
- (d)
\(\pi\times10^4\)
The gravitaion force varies inversely as the nth power of the distance. Then, the time period of a planet in circular orbit of radius a around the sun will be proportional to
- (a)
\(a^{({n-1})\over2}\)
- (b)
a2
- (c)
an/2
- (d)
\(a^{(n+1)\over 2}\)
Two equal masses 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:
- (a)
\(\pi\)G\(\rho \)mh
- (b)
\(\frac{1}{3}\)\(\pi\)G\(\rho \)mh
- (c)
\(\frac{8}{3}\)\(\pi\)G\(\rho \)mh
- (d)
\(\frac{4}{3}\)\(\pi\)G\(\rho \)mh
A missile launched with a velocity less than escape velocity, the sum of its KE and PE is always:
- (a)
+ ve
- (b)
zero
- (c)
- ve
- (d)
none of these
If g = acceleration due to gravity and V be gravitational potential at a distance r from the centre of the earth (where r> R), then what is the relation between g and V?
- (a)
g = V/r
- (b)
g = -dv/dr
- (c)
g = d2V/dr2
- (d)
g=-V2/r2
The ratio of the kinetic energy required to be given to the satellite to escape the earth's gravitational field to the kinetic energy required to be given so that the satellite moves in circular orbit just above the earth's atmosphere is:
- (a)
one
- (b)
two
- (c)
half
- (d)
infinity
A satellite is orbiting around the earth. By what percentage should we increase its velocity so as to enable it to escape away from the earth?
- (a)
41.4%
- (b)
50%
- (c)
82.8%
- (d)
100%
The distance of the geostationary satellite from the centre of the earth (radius R) is nearest to
- (a)
5R
- (b)
6R
- (c)
7R
- (d)
8R
If Rm is the radius of the moon's orbit round the earth, am the acceleration of the moon towards the centre of the earth and Re, the radius of the earth, then am is equal to: (if g is the acceleration due to gravity on the surface of the earth)
- (a)
\({ \left( \frac { { R }_{ e } }{ { R }_{ m } } \right) }g\)
- (b)
\({ \left( \frac { { R }_{ m } }{ { R }_{ e } } \right) }g\)
- (c)
\({ \left( \frac { { R }_{ m } }{ { R }_{ e } } \right) }^{ 2 }g\)
- (d)
\({ \left( \frac { { R }_{ e } }{ { R }_{ m } } \right) }^{ 2 }g\)
If a planet of given density were made larger, its force of attraction for an object on its surface would increase because of the planet's greater mass but would decrease because of greater separation from the object to the centre of the planet. Which effect predominates?
- (a)
Increase in radius
- (b)
Increase in mass
- (c)
Both affect the attraction equally
- (d)
None of the above
If the distance between the sun and the earth is 400 times the distance between the moon and the earth and gravitational pull of the sun on the earth is 170 times the gravitational pull of the earth on the moon, then the ratio of the mass of the sun to that of the moon is approximately equal to:
- (a)
2.7x 107
- (b)
4.6x109
- (c)
6.8x104
- (d)
7.4 x 104
A ball is dropped from a spacecraft revolving around the earth at a height of 120 km. What will happen to the ball?
- (a)
It will go very far in the space
- (b)
It will fall down on the earth gradually
- (c)
It will move with the same speed, tangentially to the spacecraft
- (d)
it will continue to move with the same speed along the original orbit of spacecraft
The weight of an astronaut, in an artificial satellite revolving around the earth, is:
- (a)
zero
- (b)
equal to that on the earth
- (c)
more than that on the earth
- (d)
less than that on the earth
Orbit velocity of an object of mass m is proportional to:
- (a)
m0
- (b)
m
- (c)
m2
- (d)
\(\frac{1}{m}\)
The escape velocity of a projectile on the earth's surface is 11.2 krn s-1. A body is projected out with thrice this speed. The speed of the body far away form the earth will be
- (a)
22.4 km s -1
- (b)
31.7 km s-1
- (c)
33.h km s-1
- (d)
none of these
Two spheres of masses m and M are situated in air and the gravitational force between them is F.The space around the masses is now filled with a liquid of specific gravity 3. The gravitational force will be now:
- (a)
F
- (b)
3F
- (c)
F/3
- (d)
F/9
If M is the mass of the earth and R its radius, the ratio of the gravitational acceleration and gravitational constant is:
- (a)
R2/M
- (b)
M/R2
- (c)
MR2
- (d)
M/R
A satellite is orbiting around the earth with total energy E. What will happen if the satellites' kinetic energy is made 2E?
- (a)
Radius of the orbit is doubled.
- (b)
Radius of the orbit is halved.
- (c)
Period of revolution is doubled.
- (d)
Satellite escapes away.
A non-homogeneous sphere of radius a has the following density (d) variations
d = d0 when r\(\le \)a/ 3
d = d0/2 when a/3<r5\(\le \)a
(r is the distance from the centre of the sphere) Consider the following statements:
1. Gravitational field at r = a/ 2is greater than that at r =2a.
2. Gravitational field at r = a/ 4 is greater than that at r =2a.
Which of the statements given above is/are correct?
- (a)
1 only
- (b)
2 only
- (c)
Both 1 and 2
- (d)
Neither 1 nor 2
A satellite moving around the earth in a circular orbit of radius r and speed v suddenly loses some of its energy. Then:
- (a)
r will increase and v will decrease
- (b)
both r and v will decrease
- (c)
r will decrease and v will increase
- (d)
none of the above
A satellite of mass m is orbiting the earth at a height h from its surface. If M is the mass of the earth and R its radius, then how much energy must be spent to pull the satellite out of the earth's gravitational field?
- (a)
\(\frac { 2GmM }{ { (R+h) }^{ 2 } } \)
- (b)
\(\frac { GmM }{ { 2(R+h) }^{ 2 } } \)
- (c)
\(\frac{2GmM}{(R+h)}\)
- (d)
\(\frac{GmM}{(2R+h)}\)