Question

two bodies of equal mass rest side by side. A constant force F acts on the first body and impulse I is applied on the second body along the line of action of that force. Prove that bodies meet again after a time 2I/F​

Answer 1

Given that,

Constant force = F

Impulse = I

We know that,

According to action reaction law,

The force on the first body is equals of the force on the other body and the direction of the force on the first body is opposite to the direction of the force on the second body.

If the total force is F.

So, the force is on one side is $\dfrac{F}{2}$

We need to calculate the time

Using formula of impulse

$J=F t$

Where, J= impulse

F = force

t = time

Put the value into the formula

$I=\dfrac{F}{2}\times t$

$t=\dfrac{2I}{F}$

The time is $\dfrac{2I}{F}$

Hence, That is proved.

Answer 2

Given that,

Constant force = F

Impulse = I

We know that,

According to action reaction law,

The force on the first body is equals of the force on the other body and the direction of the force on the first body is opposite to the direction of the force on the second body.

If the total force is F.

So, the force is on one side is $\dfrac{F}{2}$

We need to calculate the time

Using formula of impulse

$J=F t$

Where, J= impulse

F = force

t = time

Put the value into the formula

$I=\dfrac{F}{2}\times t$

$t=\dfrac{2I}{F}$

The time is $\dfrac{2I}{F}$

Hence, That is proved.

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