Question

A projectile is fired from the surface of the earth with a velocity of $5\, m s^{- 1}$ and angle $\theta$ with the horizontal. Another projectile fired from another planet with a velocity of $3\,ms^{ - 1}$ 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 $ms^{ - 2}$ ) is (Given $g= 9.8 \,ms^{ - 2}$)

• A. 3.5
• B. 5.9
• C. 16.3
• D. 110.8

Answer 1

The Correct Option is A

The equation of trajectory is
$y = x\, tan\, \theta - \frac{ gx^2 }{ 2 u^2 \, cos^2 \, \theta} $
where $\theta$ is the angle of projection and $u$ is the velocity with which projectile is projected.
For equal trajectories and for same angles of projection,
$ \frac{ g }{u^2 }$ = constant.
As per, question, $ \frac{ 9.8}{ 5^2 } = \frac{ g ' }{ 3^2}$
where $g'$ is acceleration due to gravity on the planet.
$g ' = \frac{ 9. 8 \times 9 }{ 25} = 3. 5 \, ms^{ - 2}$