A bob of mass '$$m$$' is suspended by a light string of length '$$L$$'. It is imparted a minimum horizontal velocity at the lowest point $$A$$ such that it just completes half circle reaching the top most position B. The ratio of kinetic energies $$\frac{(K . E)_A}{(K . E)_B}$$ is :

A block of mass $$100 \mathrm{~kg}$$ slides over a distance of $$10 \mathrm{~m}$$ on a horizontal surface. If the co-efficient of friction between the surfaces is 0.4, then the work done against friction $$(\operatorname{in} J$$) is :

The potential energy function (in $$J$$ ) of a particle in a region of space is given as $$U=\left(2 x^2+3 y^3+2 z\right)$$. Here $$x, y$$ and $$z$$ are in meter. The magnitude of $$x$$-component of force (in $$N$$ ) acting on the particle at point $$P(1,2,3) \mathrm{m}$$ is :

A ball suspended by a thread swings in a vertical plane so that its magnitude of acceleration in the extreme position and lowest position are equal. The angle $$(\theta)$$ of thread deflection in the extreme position will be :