NEET Motion in a Plane — Set 12

Question 1

A particle completes 10 revolutions in $ 5 \, \text{s} $ in a circular path of radius $ 1.5 \, \text{m} $. What is its linear speed?

Accepted Answer

Frequency $ f = \frac{n}{t} = \frac{10}{5} = 2 \, \text{Hz} $. Angular speed $ \omega = 2\pi f = 2\pi \times 2 = 4\pi \, \text{rad/s} $. Linear speed $ v = \omega R = 4\pi \times 1.5 = 6\pi \approx 18.85 \, \text{m/s} $.

Question 2

What is true about the angular speed in uniform circular motion if the period of revolution increases?

Accepted Answer

Angular speed is $ \omega = \frac{2\pi}{T} $, where $ T $ is the period. If the period increases, $ \omega $ decreases because they are inversely proportional; a longer period means fewer revolutions per unit time.

Question 3

A particle starts with velocity $ 7 \hat{j} \, \text{m/s} $ and accelerates at $ (3 \hat{i} - 2 \hat{j}) \, \text{m/s}^2 $. What is its speed after $ 2 \, \text{s} $?

Accepted Answer

Velocity $ \mathbf{v} = \mathbf{v}_0 + \mathbf{a} t $. Given: $ \mathbf{v}_0 = 7 \hat{j}, \mathbf{a} = 3 \hat{i} - 2 \hat{j}, t = 2 \, \text{s} $. $ \mathbf{v} = 7 \hat{j} + (3 \hat{i} - 2 \hat{j}) \times 2 = 6 \hat{i} + (7 - 4) \hat{j} = 6 \hat{i} + 3 \hat{j} \, \text{m/s} $. Speed $ v = \sqrt{6^2 + 3^2} = \sqrt{36 + 9} = \sqrt{45} \approx 6.71 \, \text{m/s} $.

NEET Physics: Motion in a Plane — Practice Set 12

Q1. A particle completes 10 revolutions in \( 5 \, \text{s} \) in a circular path of radius \( 1.5 \, \text{m} \). What is its linear speed?

Q2. What is true about the angular speed in uniform circular motion if the period of revolution increases?

Q3. A particle starts with velocity \( 7 \hat{j} \, \text{m/s} \) and accelerates at \( (3 \hat{i} - 2 \hat{j}) \, \text{m/s}^2 \). What is its speed after \( 2 \, \text{s} \)?

Q4. A projectile is launched at \( 18 \, \text{m/s} \) at \( 30^\circ \). What is its range? (Take \( g = 9.8 \, \text{m/s}^2 \))

Q5. What is the shape of the path followed by a projectile under the influence of gravity alone?

Q6. In motion with constant acceleration in a plane, what happens if the acceleration is opposite to the initial velocity?

Q7. In uniform circular motion, what happens to the object’s motion if its speed doubles while the radius remains constant?

Q8. What is the key difference between the velocity and acceleration vectors in uniform circular motion?

Q9. In uniform circular motion, what causes the acceleration of the object?

Q10. A particle starts from rest with a constant acceleration of \( (4 \hat{i} - 3 \hat{j}) \, \text{m/s}^2 \). What is its speed after \( 5 \, \text{s} \)?