Question

a stationary object is released from a point P at a distance 3R from the centre of the moon which has radius R and mass M. Whiich of the following gives the speed of the object on hitting the moon?
1. (2GM/3R)^1/2
2. (4GM/3R)^1/2
3. (GM/3R)^1/2
4. (GM/R)^1/2

Answer 1

Answer on Question #49237 – Physics – Mechanics | Kinematics | Dynamics

1. A stationary object is released from a point P at a distance 3R from the centre of the moon which has radius R and mass M. Which of the following gives the speed of the object on hitting the moon?

1. (2GM/3R)^1/2;

2. (4GM/3R)^1/2;

3. (GM/3R)^1/2;

4. (GM/R)^1/2.

Solution.

We must use the law of conservation and transformation of energy. The sum of the potential energy of an object and its kinetic energy remain constant:

$$- G \frac {m M}{3 R} + \frac {m \cdot v _ {0} ^ {2}}{2} = - G \frac {m M}{R} + \frac {m \cdot v _ {1} ^ {2}}{2},$$

where $m$ is the object mass, $v_{0}(v_{1})$ is its initial (final) speed.

The object was stationary, so $v_{0} = 0$.

Thus, we can find the speed of the object on hitting the moon.

$$- G \frac {M}{3 R} = - G \frac {M}{R} + \frac {v _ {1} ^ {2}}{2}, \quad \frac {v _ {1} ^ {2}}{2} = \frac {2 G M}{3 R}, \quad v _ {1} = 2 \sqrt {\frac {G M}{3 R}}.$$

Answer: 2)

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