A block is placed on a parabolic shape ramp given by equation, $y=\frac{x^2}{20}$. If the coefficient of static friction $\left(\mu_s\right)$ is 0.5 , then what is the maximum height above the ground at which the block can be placed without slipping?

Two blocks of masses 1 kg and 2 kg connected by a light rod and the system is slipping down a rough incline angle $45^{\circ}$ with the horizontal. The frictional coefficient at both the contacts is 0.4 . If the acceleration of the system is $\alpha \sqrt{2}$, the value of $\alpha$ is (use, $g=10 \mathrm{~m} / \mathrm{s}^2$ )

A time varying force acts on a ball of mass 100 g for 2 ms . The force versus time curve is shown below. If the initial speed of the ball is $10 \mathrm{~m} / \mathrm{s}$, then the speed of ball after 2 ms is

The velocity of an object of mass 2 kg is given by $\mathbf{v}=\left(8 t \hat{\mathbf{i}}+3 t^2 \hat{\mathbf{j}}\right) \mathrm{m} / \mathrm{s}$, where $t$ is time in seconds. What will be the direction of net force on the object relative to the positive direction of $X$-axis, at the instant when its magnitude is 20 N ?