B.

90°

When an object follows a circular path at a constant speed, the motion of object is called uniform circular motion. Although the speed does not vary the particle is accelerating because the velocity changes its direction at every point on circular track.

The acceleraton is centripetal, which is perpendicular to motion at every point and acts along the radius and directed towards the centre of the curved circular path.

C.

50 ms^-1

p₁ = mu = m . 20

$\therefore \left|{\mathrm{p}}_1\right| = \left|{\mathrm{p}}_2 + {\mathrm{p}}_3\right|$

$$\begin{gathered} {\mathrm{p}}_2 = \sqrt{{\mathrm{p}}_1^2 + {\left({\mathrm{p}}_2\right)}^2} \\ \frac{\mathrm{mv}}{2} = \sqrt{{\mathrm{m}}^2 {\left(20\right)}^2 + {\left(\frac{\mathrm{m}}{2} 30\right)}^2} \\ \frac{\mathrm{mv}}{2} = \frac{\mathrm{m}}{2} \sqrt{{\left(40\right)}^2 + {\left(30\right)}^2} \\ \mathrm{v} = 50 \mathrm{m}/\sec \end{gathered}$$

D.

R/4

u = v_e/2 , v_e = escape velocity of body for that planet

$$\begin{gathered} {\mathrm{h}}_{\max } = \frac{{\mathrm{u}}^2}{2\mathrm{g}} \mathrm{R} = \mathrm{radius} \mathrm{of} \mathrm{planet} \\ = \frac{{\mathrm{v}}_{\mathrm{e}}^2}{\mathrm{u} \times 2\mathrm{g}} \end{gathered}$$

Due to gravity at that planet

$$\begin{gathered} = \frac{2\mathrm{Rg}}{\mathrm{u} \times 2\mathrm{g}} {\mathrm{v}}_{\mathrm{e}} = \sqrt{2 \mathrm{Rg}} \\ {\mathrm{h}}_{\max } = \frac{\mathrm{R}}{4} \end{gathered}$$

D.

60

A is the origin from where the ball is thrown.
Let u be the velocity of projection of ball.

∴  v² = u² − 2gh            (upwards)

At B, v = 0

$\mathrm{u} = \sqrt{2\mathrm{gh}} = \sqrt{2 \times 10 \times 5} = 10 \mathrm{m}/\sec$

Ball is projected with 10 m/sec.

Time taken by ball to reach max height

          v = u − gt

          0 = 10 − 10t

⇒        t = 1 sec

In 1 sec, ball will reach the top and in next 1 sec it will reach the ground again.

∴ 1st ball reaches B in 1 sec.

 IInd ball reached B in 1 sec.

When IInd is at B, 1st is at A and so on.

∴ Number of ball projected/sec = 1

  Number of ball projected/min = 60