$A$ particle of mass $m$ falls from rest through a resistive medium having a resistive force, $F = -kv$, where $v$ is the velocity of the particle and $k$ is a constant. Which of the following graphs represents velocity $(v)$ versus time $(t)$?

$A$ particle is projected with a speed $v_0 = \sqrt{gR}$ at the bottom of a hemispherical bowl. The coefficient of friction between the particle and the hemispherical surface is $\mu = 0.5$. Then,the initial acceleration of the particle is:

In the figure,two blocks $M$ and $m$ are tied together with an inextensible and light string. The mass $M$ is placed on a rough horizontal surface with coefficient of friction $\mu$ and the mass $m$ is hanging vertically against a smooth vertical wall. The pulley is frictionless. Imagine a situation in which the given arrangement is placed inside an elevator that can move only in the vertical direction and compare the situation with the case when it is placed on the ground. When the elevator accelerates downward with $a_0 (< g)$,then

$A$ bouncing ball of mass $200 \,g$ falls from a height of $5 \,m$ onto a horizontal ground. After every impact with the ground, the velocity of the ball decreases by $\frac{1}{2}$ times. The total momentum the ball imparts to the ground after $3$ impacts is (Let $g=10 \,m/s^2$):

$A$ body of mass $2 \ kg$ is acted upon by two forces each of magnitude $1 \ N$ and inclined at $60^{\circ}$ with each other. The acceleration of the body in $m/s^2$ is $[\cos 60^{\circ}=0.5]$

$A$ ball rests upon a flat piece of paper on a table top. The paper is pulled horizontally but quickly towards the right as shown. Relative to its initial position with respect to the table,the ball:
$(1)$ remains stationary if there is no friction between the paper and the ball.
$(2)$ moves to the left and starts rolling backwards,i.e.,to the left,if there is friction between the paper and the ball.
$(3)$ moves forward,i.e.,in the direction in which the paper is pulled.
Here,the correct statement$(s)$ is/are: