Question

From the top of a tower of two stones, whose masses are in the ratio $1:2$ are thrown on straight up with an initial speed u and the second straight down with the same speed u. Then neglecting air resistance.

• A. The heavier stone hits the ground with a higher speed
• B. The lighter stone hits the ground with a higher speed
• C. Both the stones will have the same speed when they hit the ground
• D. The speed cannot be determined with the given data

Answer 1

The correct option is C Both the stones will have the same speed when they hit the ground

first stone thrown straight up with velocity u upward and gravitation acceleration acts downwards.

so first particle goes up to some height when its velocity becomes zero

and then this particle gets free fall. now when the particle goes down at level of top of tower it velocity becomes u downward and gravitation acceleration also in downward direction.

by using newtons law of motion. for first particle

$v^2=u^2+2as(a=g;s=hheightoftower){v_1}^2=u^2+2gh$

same as for second particle

initial velocity is u downward and g downward

$v^2=u^2+2as(a=g;s=hheightoftower){v_2}^2=u^2+2gh$

So both the stones have same speed at the ground level

hence option C is correct