The weight of a man in a lift moving in an upward direction with an acceleration '$a$' is $660 \text{ N}$. When the lift moves in the downward direction with the same acceleration, his weight is found to be $380 \text{ N}$. The real weight of the man when the lift is at rest is: (in $\text{ N}$)

$A$ 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 $g = 10 \text{ m/s}^2$)

$A$ monkey is sitting on the pan of a spring balance which is placed on an elevator. The maximum reading of the spring balance will be when

$A$ smooth rod of length $l$ is kept inside a trolley at an angle $\theta$ as shown in the figure. What should be the acceleration $a$ of the trolley so that the rod remains in equilibrium with respect to it?

$A$ body of mass $50 \ kg$ is suspended using a spring balance inside a lift at rest. If the lift starts falling freely,the reading of the spring balance is:

$A$ man is standing on a weighing machine placed in a lift. When stationary,his weight is recorded as $40 \, kg$. If the lift is accelerated upwards with an acceleration of $2 \, m/s^2$,then the weight recorded in the machine will be .......... $kg$ $(g = 10 \, m/s^2)$.