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A car C of ma...

Question

A car C of mass $m_{1}$ rests on a plank P of mass $m_{2}$ . The plank rests on a smooth floor. The string and pulley are ideal. The car starts and moves towards the pulley with acceleration.

m_{1} > m_{2}

, the string will remain under tension

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m_{1} < m_{2}

, the string will become slack

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m_{1} = m_{2}

, the string will have no tension, and C and P will have accelerations of equal magnitude

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C and P will have accelerations of equal magnitude if

m_{1} \geq m_{2}

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Solution

The correct options are
A If $m_{1} > m_{2}$ , the string will remain under tension
B If $m_{1} < m_{2}$ , the string will become slack
D If $m_{1} = m_{2}$ , the string will have no tension, and C and P will have accelerations of equal magnitude
Let $T$ $=$ tension in the string,
$F$ $=$ force of friction between C and P.
If the string is under tension, the acceleration of C to the right $=$ acceleration of P to the left $=$ $a$ .
$T + F = m_{1} a$
$F - T = m_{2} a$
$∴ T = \frac{1}{2} (m_{1} - m_{2}) a$ or $T > 0$ if $m_{1} > m_{2}$ .
If $m_{1} < m_{2}$ , $T$ becomes $< 0$ , i.e., it becomes slack.
If $m_{1} = m_{2}, T = 0$

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A car C of mass m1 rests on a plank P of mass m2. The plank rests on a smooth floor. The string and pulley are ideal. The car starts and moves towards the pulley with acceleration.

A car C of mass $m_{1}$ rests on a plank P of mass $m_{2}$ . The plank rests on a smooth floor. The string and pulley are ideal. The car starts and moves towards the pulley with acceleration.