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A lorry and car moving with same kinetic energy are brought to rest by applying the same retarding force. Then
a) lorry will come to rest in shorter distance
b) car will come to rest in shorter distance
c) lorry comes to rest in shorter time
d) car comes to rest in shorter time

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a, d are correct a, d

b, c are correct

only b is correct

only d is correct

answer is D.

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Detailed Solution

$Fs = ∆ K = K \Rightarrow s = \frac{K}{F}$

As, kinetic energy and retarding forces are same, the distance covered by both will be same.

$K = \frac{1}{2} {mu}^{2} \Rightarrow u \propto \frac{1}{\sqrt{m}}$

$a = - \frac{F}{m} \Rightarrow a \propto \frac{1}{m}$

$t = \frac{0 - u}{a} \Rightarrow t \propto \frac{u}{a}$

$\Rightarrow t \propto \frac{1}{\sqrt{m}} \times m = \sqrt{m}$

$\Rightarrow t \propto \sqrt{m}$

Hence, car comes to rest in shorter time.

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