NEET Motion in a Plane — Set 2

Question 1

A particle moves in a circular path of radius $ 2 \, \text{m} $ with a period of $ 1 \, \text{s} $. What is its centripetal acceleration?

Accepted Answer

Angular speed $ \omega = \frac{2\pi}{T} = \frac{2\pi}{1} = 2\pi \, \text{rad/s} $. Centripetal acceleration $ a_c = \omega^2 R = (2\pi)^2 \times 2 = 4\pi^2 \times 2 \approx 78.96 \, \text{m/s}^2 $.

Question 2

In motion with constant acceleration in a plane, how are the x- and y-components of the motion related?

Accepted Answer

For motion with constant acceleration in a plane, the x- and y-components are independent of each other. The motion can be treated as two separate one-dimensional motions along perpendicular directions, with each component governed by its own constant acceleration.

Question 3

A projectile is launched at $ 20 \, \text{m/s} $ at $ 53^\circ $. What is its maximum height? (Take $ g = 10 \, \text{m/s}^2, \sin 53^\circ = 0.8 $)

Accepted Answer

Maximum height $ h_m = \frac{(v_0 \sin \theta_0)^2}{2g} $. Given: $ v_0 = 20 \, \text{m/s}, \sin 53^\circ = 0.8, g = 10 \, \text{m/s}^2 $. $ h_m = \frac{(20 \times 0.8)^2}{2 \times 10} = \frac{16^2}{20} = \frac{256}{20} = 12.8 \, \text{m} $.

NEET Physics: Motion in a Plane — Practice Set 2

Q1. A particle moves in a circular path of radius \( 2 \, \text{m} \) with a period of \( 1 \, \text{s} \). What is its centripetal acceleration?

Q2. In motion with constant acceleration in a plane, how are the x- and y-components of the motion related?

Q3. A projectile is launched at \( 20 \, \text{m/s} \) at \( 53^\circ \). What is its maximum height? (Take \( g = 10 \, \text{m/s}^2, \sin 53^\circ = 0.8 \))

Q4. A ball is thrown horizontally at \( 5 \, \text{m/s} \) from a height of \( 20 \, \text{m} \). What is its horizontal range? (Take \( g = 10 \, \text{m/s}^2 \))

Q5. In projectile motion, what remains constant throughout the trajectory, assuming no air resistance?

Q6. A ball is thrown at \( 40 \, \text{m/s} \) at \( 30^\circ \). What is its vertical velocity at the maximum height? (Take \( g = 10 \, \text{m/s}^2 \))

Q7. A particle’s position is given by \( x = 2t + t^2 \) and \( y = 3t - 2t^2 \) (in meters and seconds). What is its speed at \( t = 2 \, \text{s} \)?

Q8. A projectile is launched at \( 18 \, \text{m/s} \) at \( 53^\circ \). What is its maximum height? (Take \( g = 9.8 \, \text{m/s}^2, \sin 53^\circ = 0.8 \))

Q9. A particle completes 6 revolutions in \( 3 \, \text{s} \) in a circular path of radius \( 1 \, \text{m} \). What is its linear speed?

Q10. A projectile is launched at \( 28 \, \text{m/s} \) at \( 45^\circ \). What is its time of flight? (Take \( g = 9.8 \, \text{m/s}^2, \sin 45^\circ = 0.707 \))

Q11. A body is projected with a speed of 20 m/s at 45°. What is the time to reach maximum height? (Take g = 10 m/s²)

Q12. What is the primary factor affecting the maximum height of a projectile launched from level ground?

Q13. In projectile motion, what is true about the acceleration at all points in the trajectory?

Q14. A particle moves in a circular path of radius \( 6 \, \text{m} \) with a frequency of \( 2 \, \text{Hz} \). What is its centripetal acceleration?

Q15. A projectile is launched at \( 42 \, \text{m/s} \) at \( 30^\circ \). What is its range? (Take \( g = 9.8 \, \text{m/s}^2, \sin 60^\circ = 0.866 \))