$A$ car is moving on a circular horizontal track of radius $10 \,m$ with a constant speed of $10 \,m/s$. $A$ bob is suspended from the roof of the car by a light wire of length $1.0 \,m$. The angle made by the wire with the vertical is (in rad)

Blocks $A$ and $B$ of mass $2\,kg$ and $4\,kg$ are suspended through a string using a pulley,inside an elevator moving downward with a constant acceleration of $2\,m/s^2$. Find the tension in the string connecting the two blocks.

$A$ 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 ..........

$A$ block of mass $m$ is resting on a wedge of angle $\theta$ as shown in the figure. The wedge is given a horizontal acceleration $a$. What is the minimum value of $a$ so that the mass $m$ falls freely?

Imagine a person standing on a weighing machine placed inside an elevator. The elevator first accelerates, then moves with a constant velocity, and finally decelerates to stop. The maximum and minimum weight recorded are $80 \ kg$ and $64 \ kg$, respectively. Find out the true mass of that person considering $g = 10 \ m/s^2$. (in $kg$)

In an elevator moving vertically up with an acceleration $g$,the force exerted on the floor by a passenger of mass $M$ is