164. According to the figure below, a object of mass $250\,\text{g}$ is placed on top of a spring whose spring constant is $2.5\,\dfrac{\text{N}}{\text{cm}}$, is released, and after hitting the spring, the spring compresses $12\,\text{cm}$. The work done by gravity on the object from the moment of release to the moment the spring reaches maximum compression is how many joules? (Air resistance is negligible and $g = 10\,\dfrac{\text{m}}{\text{s}^2}$.)
[Figure: A block resting on a spring attached to the ground]

• [(1)] $0.3$
• [(2)] $1.2$
• [(3)] $1.8$
• [(4)] $3.6$

If $g$ is the acceleration due to gravity on the earth's surface, the gain in the potential energy of object of mass $m$ raised from the surface of the earth to a height equal to the radius $R$ of the earth is
(1) 2 mgR
(2) $\frac { 1 } { 2 } \mathrm { mgR }$
(3) $\frac { 1 } { 4 } \mathrm { mgR }$
(4) mgR

A particle of mass 100 g is thrown vertically upwards with a speed of $5$ m/s. The work done by the force of gravity during the time the particle goes up is
(1) 0.5 J
(2) $-0.5$ J
(3) $-1.25$ J
(4) 1.25 J

A body of mass 50 kg is lifted to a height of 20 m from the ground in the two different ways as shown in the figures. The ratio of work done against the gravity in both the respective cases, will be: Case 1: Vertically upward Case 2: Along the ramp
(1) $1:2$
(2) $\sqrt{3}:2$
(3) $2:1$
(4) $1:1$

Q5. A body of mass 50 kg is lifted to a height of 20 m from the ground in the two different ways as shown in the figures. The ratio of work done against the gravity in both the respective cases, will be :
[Figure]
(1) $1 : 2$
(3) $2 : 1$
[Figure]
Case $- 2 \rightarrow$ Along the ramp
(2) $\sqrt { 3 } : 2$
(4) $1 : 1$

Q7. To project a body of mass $m$ from earth's surface to infinity, the required kinetic energy is (assume, the radius of earth is $R _ { E } , g =$ acceleration due to gravity on the surface of earth):
(1) $2 m g R _ { E }$
(2) $4 m g R _ { E }$
(3) $m g R _ { E }$
(4) $1 / 2 m g R _ { E }$

Q4. A satellite of $10 ^ { 3 } \mathrm {~kg}$ mass is revolving in circular orbit of radius $2 R$. If $\frac { 10 ^ { 4 } R } { 6 } J$ energy is supplied to the satellite, it would revolve in a new circular orbit of radius (use $g = 10 \mathrm {~m} / \mathrm { s } ^ { 2 } , R =$ radius of earth)
(1) $2.5 R$
(2) $3 R$
(3) $4 R$
(4) $6 R$