A cube of side \(a\) and mass \(m\) is to be tilted at point \(A\) by applying a force \(F\) as shown in…

A cube of side \(a\) and mass \(m\) is to be tilted at point \(A\) by applying a force \(F\) as shown in figure. The minimum force required is
  1. \(\mathrm{mg}\)
  2. \(\frac{2}{3} m g\)
  3. \(\frac{3}{2} m g\)
  4. \(\frac{3}{4} m g\)

Solution

The minimum force at which the cube will tilt will be when the torques of the forces acting about A will be equal.
Thus we get \(\operatorname{mg}\left(\frac{\mathrm{a}}{2}\right)=\mathrm{F}\left(\frac{3}{4} \mathrm{a}\right)\)
Thus we get
\(\mathrm{F}=\frac{2}{3} \mathrm{mg}\)
.

Asked in: JEE Mains - Rotational Motion - Chapter Test

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