If speed V, area A and force F are chosen as fundamental units, then the dimension of Young’s modulus will be

A small block starts slipping down from a point B on an inclined plane AB, which is making an angle $$\theta $$ with the horizontal section BC is smooth and the remaining section CA is rough with a coefficient of friction $$\mu $$. It is found that the block comes to rest as it reaches the bottom (point A) of the inclined plane. If BC = 2AC, the coefficient of friction is given by $$\mu $$ = ktan $$\theta $$ . The value of k is _________.

A uniform cylinder of mass M and radius R is to be pulled over a step of height a (a < R) by applying a force F at its centre ‘O’ perpendicular to the plane through the axes of the cylinder on the edge of the step (see figure). The minimum value of F required is :

Shown in the figure is rigid and uniform one meter long rod AB held in horizontal position by two strings tied to its ends and attached to the ceiling. The rod is of mass ‘m’ and has another weight of mass 2 m hung at a distance of 75 cm from A. The tension in the string at A is :