A body of mass $M$ was slowly hauled up a rough hill by a force $F$ which at each point was directed along a tangent to the hill. Work done by the force

A horizontal plane supports a plank with a block placed on it. A light elastic string is attached to the block, which is attached to a fixed point $O$. Initially, the cord is unstretched and vertical. The plank is slowly shifted to the right until the block starts sliding over it. It occurs at the moment when the cord deviates from vertical by an angle, $\mathrm{\theta }=0^{\mathrm{o}}$. Work done by the force $F$ equals

A long block $A$ is at rest on a smooth horizontal surface. A small block $B$ whose mass is half of the mass of $A$ is placed on $A$ at one end and is given an initial velocity $u$ as shown in the figure. The coefficient of friction between the blocks is $\mu$. Choose the correct statement(s).

If the particle is at rest at $\left(6, 4\right)$ at time $t=0$. The potential energy $\mathrm{\varphi }$ (in $\mathrm{joule}$) of a particle of mass $1 \mathrm{kg}$, moving in the $x-y$ plane, obeys the law $\mathrm{\varphi }=3x+4y$, where $\left(x, y\right)$ are the coordinates of the particle in $\mathrm{meter}$.

A block of mass $1 \mathrm{kg}$ is pressed against a spring of force constant $400 \mathrm{N} {\mathrm{m}}^{-1}$. The spring is compressed by $10 \mathrm{cm}$ and the block is released. Which of the following is a possible velocity of the block during subsequent motion?