Match List-I with List-II

Choose the correct answer from the options given below


(1). (a) - (ii), (b) - (i), (c) - (iv), (d) - (iii)
(2). (a) - (ii), (b) - (iv), (c) - (i), (d) - (iii)
(3). (a) - (ii), (b) - (iv), (c) - (iii), (d) - (i)
(4). (a) - (iv), (b) - (ii), (c) - (i), (d) - (iii)

Number of Attempts: 2

Correct Attempts: 1

Time Taken: 00:04

Average Time: 00:02

A particle of mass \(' m '\) is projected with a velocity \(v = kV_e\left(k < 1\right)\) from the surface of the earth.(\(V_e\) = escape velocity). The maximum height above the surface reached by the particle is

(1). \(\displaystyle R\left(\frac{k}{1 − k}\right)^2\)
(2). \(\displaystyle R\left(\frac{k}{1 + k}\right)^2\)
(3). \(\displaystyle \frac{R^2k}{1 + k}\)
(4). \(\displaystyle \frac{Rk^2}{1 - k^2}\)

Number of Attempts: 2

Correct Attempts: 1

Time Taken: 00:04

Average Time: 00:02

The radius of Martian orbit around the Sun is about 4 times the radius of the orbit of Mercury. The Martian year is 687 Earth days. Then which of the following is the length of 1 year on Mercury?

(1). 124 earth days
(2). 88 earth days
(3). 225 earth days
(4). 172 earth days

Number of Attempts: 2

Correct Attempts: 1

Time Taken: 00:04

Average Time: 00:02

A body weighs 48 N on the surface of the earth. The gravitational force experienced by the body due to the earth at a height equal to one-third the radius of the earth from its surface is :

(1). 36 N
(2). 16 N
(3). 27 N
(4). 32 N

Number of Attempts: 2

Correct Attempts: 1

Time Taken: 00:04

Average Time: 00:02

The mass of a planet is \(1/10^{th}\) that of the earth and its diameter is half that of the earth. The acceleration due to gravity on that planet is:

(1). \(19.6\, ms^{−2}\)
(2). \(9.8\, ms^{−2}\)
(3). \(4.9\, ms^{−2}\)
(4). \(3.92\, ms^{−2}\)

Number of Attempts: 2

Correct Attempts: 1

Time Taken: 00:04

Average Time: 00:02

The minimum energy required to launch a satellite of mass \(m\) from the surface of earth of mass \(M\) and radius \(R\) in a circular orbit at an altitude of \(2R\) from the surface of the earth is:

(1). \(\displaystyle \frac{5GmM}{6R}\)
(2). \(\displaystyle \frac{2GmM}{3R}\)
(3). \(\displaystyle \frac{GmM}{2R}\)
(4). \(\displaystyle \frac{GmM}{3R}\)

Number of Attempts: 2

Correct Attempts: 1

Time Taken: 00:04

Average Time: 00:02

Two bodies of mass \(m\) and \(9m\) are placed at a distance \(R\). The gravitational potential on the line joining the bodies where the gravitational field equals zero, will be ( \(G = gravitational\, constant\))

(1). \(\displaystyle \frac{-12Gm}{R}\)
(2). \(\displaystyle\frac{-16Gm}{R}\)
(3). \(\displaystyle\frac{-20Gm}{R}\)
(4). \(\displaystyle\frac{-8Gm}{R}\)

Number of Attempts: 2

Correct Attempts: 1

Time Taken: 00:04

Average Time: 00:02

A satellite is orbiting just above the surface of the earth with period \(T\). If \(d\) is the density of the earth and \(G\) is the universal constant of gravitation, the quantity \(\displaystyle \frac{3\pi}{Gd}\) represents

(1). \(T^2\)
(2). \(T^3\)
(3). \(\sqrt{T}\)
(4). \(T\)

Number of Attempts: 2

Correct Attempts: 1

Time Taken: 00:04

Average Time: 00:02

A body of mass \(60\,g\) experiences a gravitational force of \(3.0\,N\), when placed at a particular point. The magnitude of the gravitational field intensity at that point is

(1). \(0.05\,N/kg\)
(2). \(50\,N/kg\)
(3). \(20\,N/kg\)
(4). \(180\,N/kg\)

Number of Attempts: 2

Correct Attempts: 1

Time Taken: 00:04

Average Time: 00:02

The escape velocity from the Earth's surface is \(v\). The escape velocity from the surface of another planet having a radius, four times that of Earth and same mass density is

(1). \(v\)
(2). \(2v\)
(3). \(3v\)
(4). \(4v\)

Number of Attempts: 2

Correct Attempts: 1

Time Taken: 00:04

Average Time: 00:02

A body weighs \(72\,N\) on the surface of the earth. What is the gravitational force on it, at a height equal to half the radius of the earth?

(1). \(32\,N\)
(2). \(30\,N\)
(3). \(24\,N\)
(4). \(48\,N\)

Number of Attempts: 2

Correct Attempts: 1

Time Taken: 00:04

Average Time: 00:02

The work done to raise a mass \(m\) from the surface of the earth to a height \(h\), which is equal to the radius of the earth, is

(1). \(\frac{3}{2}mgR\)
(2). \(mgR\)
(3). \(2mgR\)
(4). \(\frac{1}{2}mgR\)

Number of Attempts: 2

Correct Attempts: 1

Time Taken: 00:04

Average Time: 00:02

A body weighs \(200\,N\) on the surface of the earth. How much will it weigh half way down to the centre of the earth ?

(1). \(100\,N\)
(2). \(150\,N\)
(3). \(200\,N\)
(4). \(250\,N\)

Number of Attempts: 2

Correct Attempts: 1

Time Taken: 00:04

Average Time: 00:02

The kinetic energies of a planet in an elliptical orbit about the Sun, at positions \(A\), \(B\) and \(C\) are \(K_A\), \(K_B\) and \(K_C\), respectively. \(AC\) is the major axis and \(SB\) is perpendicular to \(AC\) at the position of the Sun \(S\) as shown in the figure. Then


(1). \(K_A < K_B < K_C\)
(2). \(K_A > K_B > K_C\)
(3). \(K_B < K_A < K_C\)
(4). \(K_B > K_A > K_C\)

Number of Attempts: 2

Correct Attempts: 1

Time Taken: 00:04

Average Time: 00:02

If the mass of the Sun were ten times smaller and the universal gravitational constant were ten times larger in magnitude, which of the following is not correct?

(1). Raindrops will fall faster
(2). Walking on the ground would become more difficult
(3). Time period of a simple pendulum on the Earth would decrease
(4). ′g′ on the Earth will not change

Number of Attempts: 2

Correct Attempts: 1

Time Taken: 00:04

Average Time: 00:02

The acceleration due to gravity at a height 1 Km above the earth is the same as at a depth "d" below the surface of earth. Then

(1). d = 1 km
(2). d = 32 km
(3). d = 2 km
(4). d = 12 km

Number of Attempts: 2

Correct Attempts: 1

Time Taken: 00:04

Average Time: 00:02

Two astronauts are floating in gravitational free space after having lost contact with their spaceship. The two will

(1). move towards each other
(2). move away from each other
(3). will become stationary
(4). keep floating at the same distance between them

Number of Attempts: 2

Correct Attempts: 1

Time Taken: 00:04

Average Time: 00:02

At what height from the surface of earth the gravitation potential and the value of g are \(-\, 5.4 × 10^7J\, \text{Kg}^{−2}\) and \(6.0\,\text{ms}^{−2}\) respectively? Take the radius of earth as 6400 km.

(1). \(1400\, \text{Km}\)
(2). \(2000\, \text{Km}\)
(3). \(2600\, \text{Km}\)
(4). \(1600\, \text{Km}\)

Number of Attempts: 2

Correct Attempts: 1

Time Taken: 00:04

Average Time: 00:02

The ratio of escape velocity at earth (\(v_e\)) to the escape velocity at a planet (\(v_p\)) whose radius and mean density are twice as that of earth is

(1). \(1 : 4\)
(2). \(1 : \sqrt{2}\)
(3). \(1 : 2\)
(4). \(1 : 2\sqrt{2}\)

Number of Attempts: 2

Correct Attempts: 1

Time Taken: 00:04

Average Time: 00:02