The weight of a man in a stationary lift is $w_1$ and when it is moving downwards with uniform acceleration $a$ is $w_2$. If the ratio $w_1 : w_2 = 4 : 3$,then the value of $a$ is ($g =$ acceleration due to gravity).

Find the force $F$ required on the cart so that the $2 \ kg$ and $1 \ kg$ blocks remain stationary relative to the cart.

The free surface of oil in a tanker,at rest,is horizontal. If the tanker starts accelerating,the free surface will be tilted by an angle $\theta$. If the acceleration is $a \ m/s^2$,what will be the slope of the free surface?

$A$ child stands on a weighing machine inside a lift. When the lift is going down with acceleration $\frac{g}{3}$,the machine shows a reading $20 \ N$. When the lift goes upwards with acceleration $\frac{g}{3}$,the reading would be ($g=$ gravitational acceleration). (in $N$)

$A$ car is moving with a uniform speed on a level road. Inside the car,there is a balloon filled with helium and attached to a piece of string tied to the floor. The string is observed to be vertical. The car now takes a left turn while maintaining the same speed on the level road. The balloon in the car will:

$A$ block of mass $M$ placed inside a box descends vertically with acceleration $a$. The block exerts a force equal to one-fourth of its weight on the floor of the box. The value of $a$ will be .............