An unloaded bus can be stopped by applying brakes on straight road after covering a distance $x$ . Suppose the passengers add $50 %$ of its weight as the load and the braking force remains unchanged, how far will the bus go after the application of the brakes? (Velocity of bus in both case is same)

Zero

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1.5 x

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2 x

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2.5 x

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Solution

The correct option is B $1.5 x$
Let $m$ be mass of the bus,
$v$ be velocity of bus before application of brake.
$F$ be resistive braking force
From work energy theorem
$W = Δ K E$
$F . x = 0 - \frac{1}{2} m v^{2}$
Now due to passengers, weight of bus in increased $50 %$
Let $x^{'}$ be the new stopping distance
$F . x^{'} = \frac{1}{2} (m + \frac{50 m}{100}) v^{2} = \frac{1}{2} (1.5 m) v^{2} \Rightarrow x^{1} = 1.5 x$

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