A wooden cube is placed on a rough horizontal table, a force is applied to the cube. Gradually the force is…

A wooden cube is placed on a rough horizontal table, a force is applied to the cube. Gradually the force is increased. Whether the cube slides before toppling or topples before sliding is independent of :
  1. the position of point of application of the force
  2. the length of the edge of the cube
  3. mass of the cube
  4. Coefficient of friction between the cube and the table

Solution

For toppling $M g \frac{L}{2}=F_{1} \times h$
For sliding $\mu M g=F_{2}$
For sliding to occur first
$F_{1}>F_{2}$
or $\frac{m g L}{2}>\mu M g$ or $L>2 \mu h$

Asked in: JEE Mains - Rotational Motion - Test 2

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