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Question

# A spool is pulled at an angle θ with the horizontal on a rough horizontal surface as shown in the figure. If the spool remains at rest, the angle θ is

A
60
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B
45
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C
20
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D
30
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Solution

## The correct option is B 45∘Let F is the applied force and f is the induced frictional force. Since, the spool is at rest even after applying force F. So, we can balance the component of applied force with the induced frictional force f in the horizontal direction. So, we can write the force balance equation along horizontal direction as, Fcosθ=f ∴cosθ=fF.....(1) Since the spool is at rest and also not rotating, so the total torque about the centre is zero, →τ=0........(2) [→τ=→r×→F=rFsinδ^η] Since, here δ is 90∘. So, from (2), we can write, ⇒1×F−√2×f=0 ⇒fF=1√2....(3) From (1) and (3), cosθ=1√2 ∴θ=45∘ Hence, option (b) is correct answer.

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