AIEEE 2006 Mock Test

The potential energy of a $1\text{kg}$ particle free to move along the $x$ -axis is given by $V(x)=\left(\frac{x^4}{4}-\frac{x^2}{2}\right)\text{J}$. The total mechanical energy of the particle is $2\text{J}$. Then, the maximum speed (in m/s) is:

A force of $-F\hat{k}$ acts on $O$, the origin of the coordinate system. The torque about the point $(1,-1,0)$ is:

A thin circular ring of mass $m$ and radius $R$ is rotating about its axis with a constant angular velocity $\omega$. Two objects each of mass $M$ are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity ${\omega }^{\prime }$:

The terminal speed of a sphere of gold (density $=19.5{\text{kg/m}}^3$) is $0.2\text{m/s}$ in a viscous liquid (density $=1.5{\text{kg/m}}^3$). Find the terminal speed of a sphere of silver (density $=10.5{\text{kg/m}}^3$) of the same size in the same liquid.

Work of $146\text{kJ}$ is performed in order to compress one kilo mole of gas adiabatically and in this process the temperature of the gas increases by $7^{\circ }\text{C}$. The gas is: ($R=8.3{\text{J mol}}^{-1}{\text{K}}^{-1}$)