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Question

In the following figure, the force F is gradually increased from zero. Draw the graph between the magnitude of F and the tension T in the string. The coefficient of static friction between the block and the ground is μ. Assume coefficient of kinetic friction and that of static friction to be equal.


A

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B

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C

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D

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Solution

The correct option is B


As the external force F is gradually increased from zero, it is compensated by the friction and the string bears no tension. Mathematically,

F-fr=0 (where the force of friction fr<μmg)

When limiting friction is achieved by increasing force F to a value till μmg, then

F-μmg > 0. So, tension will come to action

F-μmg-T=0. So, when F<μmg, the friction is static and it is equal to F, and when F>μmg, the tension in the string becomes Fμmg. As you can see, that tension will now increase linearly with F and the slope will be 1. Hence, option (b) is correct.


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