Moments

All Questions
Consider a uniform cubical box of side a on a rough floor that is to be moved by applying minimum possible force F at a point b above its centre of mass (see figure). If the coefficient of friction is $\mu = 0.4$, the maximum possible value of $100 \times \frac { b } { a }$ for a box not to topple before moving is $\_\_\_\_$
A triangular plate is shown. A force $\vec { F } = 4 \hat { \mathrm { i } } - 3 \hat { \mathrm { j } }$ is applied at point $P$. The torque at point $P$ with respect to point $O$ and $Q$ are:
(1) $- 15 - 20 \sqrt { 3 } , 15 - 20 \sqrt { 3 }$
(2) $15 + 20 \sqrt { 3 } , 15 - 20 \sqrt { 3 }$
(3) $15 - 20 \sqrt { 3 } , 15 + 20 \sqrt { 3 }$
(4) $- 15 + 20 \sqrt { 3 } , 15 + 20 \sqrt { 3 }$