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Question

Figure shows a block of mass m placed on a horizontal surface. The coefficient of static friction between the block and the surface is μ. The maximum force F that can be applied at point O such that the block does not slip on the surface is

  1. μ mg sin θ
  2. μ mg cos θ
  3. μ mg tan θ
  4. μ mg


Solution

The correct option is C μ mg tan θ
Let T1 and T2 be the tensions in the string as shown in Fig.

Here frictional force f=μmg. Since the system is in static equilibrium, no net force acts at a point O and on block m. Hence, acceleration of O and m is zero.
For point O:T2=T1 cos θ
and           F=T1 sin θ      (1)
For block: T2=f
 T1 cos θ=μmg      (2)
Dividing (1) and (2) we get
F=μmg tan θ       (3)
If force F exceeds the value given by (3), the block will begin to slide on the surface. So the correct choice is (c).

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