$A$ man of weight $mg$ is in a lift moving up with an acceleration of $4g$. The apparent weight of the man in the lift is:

$A$ block of mass $m$ is in contact with the cart $C$ as shown in the figure. The coefficient of static friction between the block and the cart is $\mu$. The acceleration $\alpha$ of the cart that will prevent the block from falling satisfies:

$A$ trolley is sliding freely down an inclined plane as shown in the figure. The angle $(\alpha)$ that the string of the pendulum makes with the ceiling of the trolley is equal to ..........

Two blocks of masses $m_1$ and $m_2$ are connected with a massless unstretched spring and placed over a plank moving with an acceleration '$a$' as shown in the figure. The coefficient of friction between the blocks and the platform is $\mu$.

$A$ piece of wire is bent in the shape of a parabola $y=kx^2$ ($y$-axis vertical) with a bead of mass $m$ on it. The bead can slide on the wire without friction. It stays at the lowest point of the parabola when the wire is at rest. The wire is now accelerated parallel to the $x$-axis with a constant acceleration $a$. The distance of the new equilibrium position of the bead,where the bead can stay at rest with respect to the wire,from the $y$-axis is

$A$ man has a mass of $80 \text{ kg}$. He stands on a weighing scale in a lift which is moving upwards with a uniform acceleration of $6 \text{ m/s}^2$. What would be his apparent weight in $\text{kg}$? (Take $g = 10 \text{ m/s}^2$)