The coefficient of static friction between a block of mass m and an incline is $μ_{s}$ = 0.3. What can be the maximum angle θ of the incline with the horizontal so that the block does not slip on the plane? (Also called angle of repose)

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What is the torque on the pivot of a pendulum of length R and mass m , when the mass is at an angle θ?

The correct option is C mgR sin θThe torque of force about a point is given by τ=r×F.Here force is mg downwards and vector r is R with the angle between force and position vector being θ.Hence torque on the pivot=mg×R×sinθ=mgRsinθ

What is the torque on the pivot of a pendulum of length $R$ and mass $m$ , when the mass is at an angle $θ$ ?

The correct option is C $m g R s i n$ $θ$
The torque of force about a point is given by $τ = r \times F$ .
Here force is $m g$ downwards and vector $r$ is $R$ with the angle between force and position vector being $θ$ .
Hence torque on the pivot= $m g \times R \times sin θ = m g R s i n θ$