A block of mass 2 kg rests at one end of a 3…

A block of mass 2 kg rests at one end of a 3 m long plank of mass 4 kg lying on a smooth horizontal floor. The coefficient of friction between block…

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A block of mass

2\ \mathrm{kg}

rests at one end of a

3\ \mathrm{m}

long plank of mass

4\ \mathrm{kg}

lying on a smooth horizontal floor. The coefficient of friction between block and plank is

0.3

. A horizontal force of

15\ \mathrm{N}

is applied to the block along the plank. Take

g=10\ \mathrm{m\,s^{-2}}

. The block leaves the other end of the plank after a time

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Answer: (B) $\sqrt{2}\ \mathrm{s}$

First test for slipping. The largest acceleration friction can give the plank is

\mu m g/M=0.3\times2\times10/4=1.5\ \mathrm{m\,s^{-2}}

. If both moved together the acceleration would be

15/6=2.5\ \mathrm{m\,s^{-2}}>1.5

, so the block slides. Block:

a_1=(15-6)/2=4.5\ \mathrm{m\,s^{-2}}

. Plank:

a_2=6/4=1.5\ \mathrm{m\,s^{-2}}

. The relative acceleration is

3\ \mathrm{m\,s^{-2}}

and the relative displacement must be the plank length:

3=\tfrac12(3)t^2

, so

t^2=2

and

t=\sqrt2\ \mathrm{s}

. Using

a=15/6

without checking for slipping would give a wrong answer.

Original question written in the JEE Main 2016 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake