Question

Identical guns fire identical bullets horizontally at the same speed from the same height above level planes, one on the earth and one on the moon. Which of the following three statement(s) is/are true?
I. The horizontal distance traveled by the bullet is greater for the moon.
II. The time of flight is less for the bullet on the earth.
III. The velocity of the bullets at impact are the same.

• A. III only
• B. II only
• C. I and II only
• D. I and III only

Answer 1

The correct option is C

I and II only

Hint: The gravitational pull of the earth is six times the gravitational pull of the moon.

Explanation for the correct option:

Option C:

Statement I:

1. Acceleration due to gravity on the moon, $g_M=\frac{g_E}{6}$. Here, $g_E$ is the acceleration due to gravity on earth.
2. The horizontal distance covered during a projectile motion is called range, $R=\frac{u^2\sin 2\theta }{g}$. Therefore, $R\propto \frac{1}{g}$.
3. As $g_E>g_M$, therefore the horizontal distance traveled by the bullet (range) is greater for the moon.
4. Hence, this statement is true.

Statement II:

1. The formula used for calculating the time of flight during a projectile motion, $T=\frac{2u\sin \theta }{g}$. Therefore, $T\propto \frac{1}{g}$.
2. As $g_E>g_M$, therefore the time of flight is less for the bullet on the earth.
3. Hence, this statement is true.

Statement III:

1. The $y$ component of velocity, $v_y=u\sin \theta -gt$. Therefore, $v\propto g$.
2. As $g_E>g_M$, The velocity of the bullet on the earth will be lesser at impact.
3. Hence, this statement is not true.

Hence, statements I and II are correct. Hence, option C is the correct answer.