NEET Motion in a Plane — Set 14

Question 1

A car moves at 72 km/h in a circular path of radius 50 m. What is its centripetal acceleration? (Take 72 km/h = 20 m/s)

Accepted Answer

Centripetal acceleration a_c = v² / R. Given: v = 20 m/s, R = 50 m. a_c = (20)² / 50 = 400 / 50 = 8 m/s².

Question 2

A particle moves with an initial velocity of $ 4 \hat{i} \, \text{m/s} $ and an acceleration of $ (2 \hat{i} - 3 \hat{j}) \, \text{m/s}^2 $. What is its speed after $ 3 \, \text{s} $?

Accepted Answer

Velocity $ \mathbf{v} = \mathbf{v}_0 + \mathbf{a} t $. Given: $ \mathbf{v}_0 = 4 \hat{i}, \mathbf{a} = 2 \hat{i} - 3 \hat{j}, t = 3 \, \text{s} $. $ \mathbf{v} = 4 \hat{i} + (2 \hat{i} - 3 \hat{j}) \times 3 = 4 \hat{i} + 6 \hat{i} - 9 \hat{j} = 10 \hat{i} - 9 \hat{j} \, \text{m/s} $. Speed $ v = \sqrt{10^2 + (-9)^2} = \sqrt{100 + 81} = \sqrt{181} \approx 13.45 \, \text{m/s} $.

Question 3

A ball is thrown at $ 15 \, \text{m/s} $ at $ 60^\circ $. What is its vertical velocity after $ 1 \, \text{s} $? (Take $ g = 10 \, \text{m/s}^2, \sin 60^\circ = 0.866 $)

Accepted Answer

Vertical velocity $ v_y = v_0 \sin \theta_0 - g t $. Given: $ v_0 = 15 \, \text{m/s}, \sin 60^\circ = 0.866, t = 1 \, \text{s}, g = 10 \, \text{m/s}^2 $. $ v_y = 15 \times 0.866 - 10 \times 1 = 12.99 - 10 \approx 2.99 \, \text{m/s} $.

NEET Physics: Motion in a Plane — Practice Set 14

Q1. A car moves at 72 km/h in a circular path of radius 50 m. What is its centripetal acceleration? (Take 72 km/h = 20 m/s)

Q2. A particle moves with an initial velocity of \( 4 \hat{i} \, \text{m/s} \) and an acceleration of \( (2 \hat{i} - 3 \hat{j}) \, \text{m/s}^2 \). What is its speed after \( 3 \, \text{s} \)?

Q3. A ball is thrown at \( 15 \, \text{m/s} \) at \( 60^\circ \). What is its vertical velocity after \( 1 \, \text{s} \)? (Take \( g = 10 \, \text{m/s}^2, \sin 60^\circ = 0.866 \))

Q4. A car moves in a circle of radius \( 10 \, \text{m} \) with a speed of \( 5 \, \text{m/s} \). What is its angular speed?

Q5. What is true about the potential energy of a projectile at its maximum height?

Q6. A ball is projected horizontally at \( 5 \, \text{m/s} \) from a height of \( 125 \, \text{m} \). What is the time of flight? (Take \( g = 10 \, \text{m/s}^2 \))

Q7. A particle moves with a constant acceleration of \( (3 \hat{i} - 2 \hat{j}) \, \text{m/s}^2 \) from rest. What is the magnitude of its velocity after \( 4 \, \text{s} \)?

Q8. An object in uniform circular motion has a period of \( 2 \, \text{s} \) and a radius of \( 8 \, \text{m} \). What is its centripetal acceleration?

Q9. A projectile is launched at \( 40 \, \text{m/s} \) at \( 45^\circ \) from a height of \( 10 \, \text{m} \). What is its range? (Take \( g = 10 \, \text{m/s}^2, \sin 45^\circ = 0.707 \))

Q10. In uniform circular motion, what is the effect of increasing the radius while keeping the speed constant?