NEET Motion in a Plane — Set 8

Question 1

A particle moves in a circle of radius $ 5 \, \text{m} $ with an angular speed of $ 2 \, \text{rad/s} $. What is its centripetal acceleration?

Accepted Answer

Centripetal acceleration $ a_c = \omega^2 R $. Given: $ \omega = 2 \, \text{rad/s}, R = 5 \, \text{m} $. $ a_c = 2^2 \times 5 = 4 \times 5 = 20 \, \text{m/s}^2 $.

Question 2

An object moves in a circle of radius 2 m with a constant speed of 4 m/s. What is its angular speed?

Accepted Answer

Angular speed ω = v / R. Given: v = 4 m/s, R = 2 m. ω = 4 / 2 = 2 rad/s.

Question 3

A ball is dropped from a height of $ 44.1 \, \text{m} $ with a horizontal speed of $ 7 \, \text{m/s} $. What is its speed on hitting the ground? (Take $ g = 9.8 \, \text{m/s}^2 $)

Accepted Answer

Vertical velocity: $ v_y = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 44.1} = \sqrt{863.28} \approx 29.38 \, \text{m/s} $. Horizontal velocity: $ v_x = 7 \, \text{m/s} $. Speed $ v = \sqrt{v_x^2 + v_y^2} = \sqrt{7^2 + 29.38^2} = \sqrt{49 + 863.28} = \sqrt{912.28} \approx 30.2 \, \text{m/s} $.

NEET Physics: Motion in a Plane — Practice Set 8

Q1. A particle moves in a circle of radius \( 5 \, \text{m} \) with an angular speed of \( 2 \, \text{rad/s} \). What is its centripetal acceleration?

Q2. An object moves in a circle of radius 2 m with a constant speed of 4 m/s. What is its angular speed?

Q3. A ball is dropped from a height of \( 44.1 \, \text{m} \) with a horizontal speed of \( 7 \, \text{m/s} \). What is its speed on hitting the ground? (Take \( g = 9.8 \, \text{m/s}^2 \))

Q4. A cyclist moves east at \( 18 \, \text{m/s} \) while the wind blows south at \( 24 \, \text{m/s} \). What is the magnitude of the relative velocity of the wind with respect to the cyclist?

Q5. A particle starts with velocity \( 5 \hat{i} \, \text{m/s} \) and accelerates at \( (-3 \hat{j}) \, \text{m/s}^2 \). What is its displacement magnitude after \( 2 \, \text{s} \)?

Q6. A particle in circular motion has a centripetal acceleration of \( 36 \, \text{m/s}^2 \) and radius \( 2 \, \text{m} \). What is its speed?

Q7. A car moves north at \( 12 \, \text{m/s} \) while a wind blows east at \( 5 \, \text{m/s} \). What is the magnitude of the car’s velocity relative to the ground?

Q8. What is the effect on the range of a projectile if the launch angle is increased beyond 45° on level ground?

Q9. A ball is thrown at \( 20 \, \text{m/s} \) at \( 45^\circ \) from a height of \( 5 \, \text{m} \). What is its range? (Take \( g = 10 \, \text{m/s}^2 \))

Q10. An object in uniform circular motion has a centripetal acceleration of 16 m/s² and a radius of 4 m. What is its linear speed?