A hammar of mass $1 k g$ strike on the head of a nail with a velocity of $2 m s^{- 1}$ . It drives the nail $0.01 m$ into a wooden block. Find the force applied by the hammer and the time of impact.

200 N; 10^{- 2} s e c

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100 N; 10^{- 3} s e c

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300 N; 10^{- 2} s e c

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400 N; 10^{- 3} s e c

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Solution

The correct option is C $200 N; 10^{- 2} s e c$ .
mass (m)= $1 k g$

Initial velocity (u) = $2 m / s$

distance covered (s)= $0.01 m$

using (3)rd equation of motion

$v^{2} = u^{2} = 2 a s$

$∴$ final velocity $(v) = 0$ (nail does not move further)

$0 = (2)^{2} + 2 a \times (0.01)$

$a = - 200 m / s^{2}$

Force of impact i..e. applied by hammer

$F = m a$

$= (1 k g) (200 m / s^{2})$

$F = 200 N$

Now, using (1) st equation of motion

$v = u + a t$

$∵ v = 0$

$0 = 2 + (- 200) t$

$t = \frac{- 2}{- 200}$

$t \Rightarrow 10^{- 2} s e c$

Hence, A is correct option.

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