Two books of mass 1 kg each are kept on a table, one over the other. The coefficient of friction on every pair of contacting surfaces is 0.3. the lower book is pulled with a horizontal force F. the minimum value of F for which slip occurs nbetween the two books is

A 1 kg mass of clay, moving with a velocity of 10 m/s, strikes a stationary wheel and sticks to it. The solid wheel has a mass of 20 kg and a radius of 1 m. assuming that the wheel and the ground are both rigid and that the wheel is set into pure rolling motion, the angular velocity of the wheel immediately after the impact is approximately

The velocity components in the $$x$$ and $$y$$ directions of a two dimensional potential flow are $$u$$ and $$v$$, respectively. Then $${{\partial u} \over {\partial y}}$$ is equal to

A leaf is caught in a whirlpool. At a given instant, the leaf is at a distance of $$120$$ $$m$$ from the centre of the whirlpool. The whirlpool can be described by the following velocitry distribution ;
$${V_r} = - \left( {{{60 \times {{10}^3}} \over {2\pi r}}} \right)m/s$$
and $${V_\theta } = - \left( {{{300 \times {{10}^3}} \over {2\pi r}}} \right)m/s.$$

Where $$r$$ (in meters) is the distance from the centre of the whirlpool . What will be the distance of the leaf from the centre when it has moved through half a revolution?