$A$ car is moving on a plane inclined at $30^{\circ}$ to the horizontal with an acceleration of $10 \, ms^{-2}$ parallel to the plane upward. $A$ bob is suspended by a string from the roof of the car. The angle in degrees which the string makes with the vertical is ...... . (Take $g = 10 \, ms^{-2}$)

$A$ frictionless wire $AB$ is fixed on a circle of radius $R$. $A$ very small bead slips on this wire. The time taken by the bead to slip from $A$ to $B$ is:

$A$ block is kept on a fixed smooth wedge whose vertical section is a curve $y = \frac{x^2}{\sqrt{3}}$ as shown in the figure,where $x$ represents the horizontal direction and $y$ represents the vertical direction. When released from a point where $y = \frac{1}{4\sqrt{3}}$,what will be its acceleration? $(g = 10 \ m/s^2)$

$A$ body of mass $5\,kg$ is suspended by a spring balance on an inclined plane as shown in the figure. The spring balance measures ............ $N$.

For the given system, the acceleration of the system is ........... $ms^{-2}$ $(\sin 37^\circ = 0.60, \sin 53^\circ = 0.80)$.

Two masses $M_1$ and $M_2$ are arranged as shown in the figure. Let '$a$' be the magnitude of the acceleration of the system. If the mass of $M_1$ is doubled and that of $M_2$ is halved,then the new acceleration of the system is (Treat all surfaces as smooth; masses of pulley and rope are negligible).