A) \[\frac{mg}{2}\]
B) \[\frac{\sqrt{3}}{4}mg\]
C) mg
D) 0
Correct Answer: D
Solution :
If student use, \[f=\mu \,mg\cos \theta \]\[=\frac{1}{2}\times mg\cos {{30}^{o}}=\frac{\sqrt{3}}{4}mg\] Hence option [B] but correct answer is [D]. All forces on sphere pass through its centre except the force of friction exerted by inclined plane. Since net torque on sphere in equilibrium about its centre is zero, the torque on sphere due to frictional force about its centre must be zero. Hence frictional force on cylinder is zero.
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