There is a rectangular plate of mass M kg of dimensions ( $a \times b$ ). The plate is held in horizontal position by striking $n$ small balls each of mass m per unit area per unit time. These are striking in the shaded half region of the plate. The balls are colliding elastically with velocity $v$. What is $v$ ?

In an insulated vessel, 0.05 kg steam at 373 K and 0.45 kg of ice at 253 K are mixed. Then, find the final temperature of the mixture.

In hydrogen-like atom $(z=11)$, $n$th line of Lyman series has wavelength A equal to the de Broglie's wavelength of electron in the level from which it originated. What is the value of $n$ ?

A circular disc with a groove along its diameter is placed horizontally. A block of mass 1 kg is placed as shown. The coefficient of friction between the block and all surfaces of groove in contact is $\mu=\frac{2}{5}$. The disc has an acceleration of $25 \mathrm{~m} / \mathrm{s}^2$. Find the acceleration of the block with respect to disc.