JEE Main Physics - Gravitation
Exam Duration: 60 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
a pendulum which is a seconds pendulum on the earth, is placed in a communication satellite moving in its synchronous orbit. it will
- (a)
oscillate with time period of 2 s
- (b)
oscillate with time period less than 2 s
- (c)
oscillate with time period more than 2 s
- (d)
not oscillate at all
potentail energy of a system consisting of four equal- mass particles M located at the corners of a square having sides of length L is
- (a)
\(\frac { -{ GM }^{ 2 }(4+\sqrt { 2 } ) }{ d } \)
- (b)
\(-4\frac { { GM }^{ 2 } }{ d } \)
- (c)
\(\frac { -\sqrt { 2\quad { GM }^{ 2 } } }{ d } \)
- (d)
none of the above
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
the accelaration on the surface of the varies
- (a)
directly with longitude
- (b)
directly with latitude
- (c)
inversly with longitude
- (d)
inversly with latitude
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
gravitational mass is proportional to gravitational
- (a)
field
- (b)
force
- (c)
intensity
- (d)
all of these
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
There is a mine of depth 2km. The conditions as compared to those at the surface of the earth are
- (a)
lower value of g
- (b)
higher value of g
- (c)
higher value of g
- (d)
lower value of g
A projectile is fired from the surface of the earth with the velocity CVe, where, Ve is the esape velocity. The h is maximum height from the earth's centre to which it rises up and R is the radius of the earth, then
- (a)
h=\(R\over{1-c^2}\)
- (b)
\(h={R\over c^2}\)
- (c)
\(h={2R\over c}\)
- (d)
\(h={2R\over{1-c^2}}\)
Match the statement given in column I with their formula given in column II and choose the correct option from the choices given below.
Column I | Column II |
---|---|
A. Gravitational binding energy | 1. g-R\(\omega^2\) |
B. Escape velocity | 2. \(GMm\over R\) |
C. Acceleration due to gravity at equation | 3. \(\sqrt2 V_0\) |
- (a)
A B C 1 2 3 - (b)
A B C 2 3 1 - (c)
A B C 3 2 1 - (d)
A B C 1 3 2
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
If suddenly the gravitational force of attraction between the earth and a satellite revolving around it becomes zero, then the satellite will,
- (a)
continue to move in its orbit with same speed
- (b)
move tangentially to the original orbit with the same speed
- (c)
become stationary in its orbit
- (d)
move towards the earth
A synchronous relay satellite reflects TV signals and transmit.s TV programmes from one part of the world to the other because its:
- (a)
period of revolution is greater than the period of rotation of the earth about its axis
- (b)
period of revolution is less than the period of rotation of the earth about its axis
- (c)
period of revolution is equal to the period of rotation of the earth about its axis
- (d)
mass is less than the mass of the earth
In case of a solid sphere, where is its gravitational potential minimum?
- (a)
At the centre of the sphere
- (b)
At the surface of the sphere
- (c)
At infinity
- (d)
At mid-point between the centre and surface of the sphere
A tunnel is dug along a diameter of the earth of mass Me and radius Re. The force on a particle of mass m placed in the tunnel at a distance rfrom the centre is:
- (a)
\(\frac { G{ M }_{ e }m }{ { R }_{ e }^{ 3 } } r\)
- (b)
\(\frac { G{ M }_{ e }m }{ { R }_{ e }^{ 3 }r } \)
- (c)
\(\frac { G{ M }_{ e }m{ R }_{ e }^{ 3 } }{ r } \)
- (d)
\(\frac { G{ M }_{ e }m }{ { R }_{ e }^{ 2 } } r\)
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.
The orbital velocity at a height h above the surface of the earth is 90% of that near the surface of the earth. If the escape velocity at the surface of the earth be v, then its value at the height h will be:
- (a)
0.99 \(\upsilon \)
- (b)
0.90 \(\upsilon \)
- (c)
0.81 \(\upsilon \)
- (d)
0.11 \(\upsilon \)
hydrogen balloon released on the moon would:
- (a)
climb with an acceleration of \(\frac{9.8}{6}\)m s-2
- (b)
climb with an acceleration of 9.8 x 6 m s-2
- (c)
neither climb nor fall
- (d)
fall with an acceleration of \(\frac{9.8}{6}\) m s-2
If the earth were to suddenly contract to half the present radius (without any external torque acting on it), by how much would the day be decreased? [Assume the earth to be a perfect solid sphere of moment of inertia (2/5)MR2]
- (a)
8 hours
- (b)
6 hours
- (c)
4 hours
- (d)
2 hours
If go, g h and g d be the acceleration due to gravity at the earth's surface, at height h and at a depth d respectively, then:
- (a)
g0> gh and g0> gd
- (b)
g0 < gh and g0 < gd
- (c)
g0> gh and g0 < gd
- (d)
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 escape velocity for a body projected vertically upwards from the surface of the earth is II kmlsec. If the body is projected at an angle of 45° with the vertical, the escape velocity will be:
- (a)
11/\(\sqrt{2}\) km/sec
- (b)
11\(\sqrt{2}\) km/sec
- (c)
2 km/sec
- (d)
11 km/sec
The depth at which the value of acceleration due to gravity becomes 1/n times the value at the surface is: (R be the radius of the earth)
- (a)
R/n
- (b)
R/n2
- (c)
R(n - 1)/n
- (d)
Rn/(n - 1)
- (e)
Rn
At what height h above the earth, the value of g becomes g/2? (R =Radius of the earth)
- (a)
3R
- (b)
\(\sqrt{2}\)R
- (c)
(\(\sqrt{2}\)-1)R
- (d)
\(\frac{1}{\sqrt{2}}\)R
How many times more, the mass of the original star is to be larger than that of the sun for the formation of 'Black Hole'?How many times more, the mass of the original star is to be larger than that of the sun for the formation of 'Black Hole'?
- (a)
2
- (b)
6
- (c)
8
- (d)
10
A satellite is moving around the earth with speed \(\upsilon\) in a circular orbit of radius r. If the orbit radius is decreased by 1%, its speed will:
- (a)
increase by 1%
- (b)
increase by 0.5%
- (c)
decrease by 1%
- (d)
decrease by 0.5%
A cosmonaut is orbiting the earth in a spacecraft at an altitude h = 630 km with a speed of 8 km/s. If the radius of the earth is 6400 km, the acceleration of the cosmonaut is:
- (a)
9.10 m/s2
- (b)
9.80 m/s2
- (c)
10.0 m/s2
- (d)
9.8b m/s2
The density of newly discovered planet is twice that of the earth. The acceleration due to gravity at the surface of the planet is equal to that at the surface ofthe earth. If the radius of the earth is R, the radius of the planet would be:
- (a)
2 R
- (b)
4 R
- (c)
\(\frac{1}{4}\)R
- (d)
\(\frac{1}{2}\)R