$A$ cork is submerged in water by a spring attached to the bottom of a bowl. When the bowl is kept in an elevator moving with an acceleration $a$ downwards, the length of the spring:

The weight of a man in a lift moving with the same acceleration upwards is $608 \ N$,while the weight of the same man in the lift moving downwards with the same acceleration is $368 \ N$. His normal weight is ............ $N$.

$A$ circular table is rotating with an angular velocity of $\omega \text{ rad/s}$ about its axis (see figure). There is a smooth groove along a radial direction on the table. $A$ steel ball is gently placed at a distance of $1 \text{ m}$ on the groove. All the surfaces are smooth. If the radius of the table is $3 \text{ m}$,the radial velocity of the ball with respect to the table at the time the ball leaves the table is $x \sqrt{2} \omega \text{ m/s}$,where the value of $x$ is............

$A$ girl drops an apple from the window of a train which is moving on a straight track with speed increasing at a constant rate. The trajectory of the falling apple as seen by the girl is

$A$ wedge $Y$ with mass of $10 \text{ kg}$ has all frictionless surfaces, and the inclined surface makes an angle of $37^{\circ}$ with the horizontal. $A$ block $X$ with mass $2 \text{ kg}$ is placed at the highest point of the wedge as shown in the figure and is at rest. At $t=0$, the wedge $Y$ is pulled toward the right with a constant force $f$ of $24 \text{ N}$. Taking the block $X$ at rest at $t=0$, the time taken by it to slide down $8.8 \text{ m}$ on the slope, while $Y$ is in motion, is . . . . . . s. (Take $\tan(37^{\circ}) = 3/4$ and $g = 10 \text{ m/s}^2$)

The readings shown in two extended spring balances,$S_1$ and $S_2$,are $60\,kg$ and $30\,kg$ respectively. The lift is accelerating upward with an acceleration of $10\,m/s^2$. The mass $m$ is stationary with respect to the lift. Then the mass of the block will be ......... $kg$. (Take $g = 10\,m/s^2$)