A body of mass M at rest explodes into 3...

A body of mass M at rest explodes into 3 pieces, A,B and C of masses `M/4,M/4` and `M/2` respectively. A and B move in perpendicular directions with velocities 5m/s and 12 m/s respectively. What is the speed of the third piece?

3.5m/s

5.5m/s

6.5m/s

8m/s

Text Solution

Verified by Experts

The correct Answer is:

The time taken by the stone to reach the floor is ` t= ( s)/(u) = ( 10)/( 2) = 5s `
The acceleration due to gravity is not to be considered in the gravity free space.
Similarly to bullet -rifle problem, we will apply the conservation of linear momentum.
Momentum of the stone `+` momentum of the man= 0 or `m_(1) u_(1)+ m_(2) u_(2) = 0`
`:. 0.5 xx 2 = - 50 xx u_(2)`
`:. u _(2) = - (1)/( 50) m//s`
`:.` The -ve sign shows the upward velocity of the man .
`:.` In 5s, the man will move upwards through a distance of `(1)/( 50) xx 5 =0.1 m` .
`:.` The man will be at a distance of `( 10 + 0.1 ) = 10.1 m ` above the floor.

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