Question

A projectile is fired from the surface of the earth with a velocity of 5 m s^-1  and angle θ  with the horizontal. Another projectile fired from another planet with a velocity of 3 m s^-1 at the same angle follows a trajectory which is identical with the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet is (in m s^-2) is (Given g = 9.8 ms^-2)

(a) 3.5

(b) 5.e

(c) 16.3

(d) 110.8

Answer 1

Correct option (a) 3.5

Explanation:

The equation of trajectory is

where θ is the angle of projection and u is the velocity with which projectile is projected. For equal trajectories and for same angles of projection,

g/u² = constant

 As per question, 9.8/5² = g'/3²

where g' is acceleration due to gravity on the planet

g' = 9.8 x 9/25 = 3.5 ms^-2