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Impulsive Forces in Collision

A body moves ...

Question

A body moves on a rough horizontal surface with acceleration $a$ when it is subjected to a horizontal force. If the applied force is doubled, it moves with acceleration

A

equal to

2 a

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B

less than

2 a

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C

greater than

2 a

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D

equal to

a

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Solution

The correct option is D greater than $2 a$
$F - f = m a_{1}$
$a_{1} = a$ which is given
$F = f + m a_{1}$
Now applied force is doubled therefore
$2 F - f = m a_{2}$
$m a_{2} = 2 (f + m a_{1}) - f$
This gives $m a_{2} = f + m a_{1} + m a_{1} = f + 2 m a_{1}$
Therefore, clearly, $a_{2} > 2 a_{1}$
$a_{2} > 2 a$

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