NEET Motion in a Plane — Set 6

Question 1

A particle moves in a circular path of radius $ 1 \, \text{m} $ completing 3 revolutions in $ 6 \, \text{s} $. What is its centripetal acceleration?

Accepted Answer

Frequency $ f = \frac{n}{t} = \frac{3}{6} = 0.5 \, \text{Hz} $. Angular speed $ \omega = 2\pi f = 2\pi \times 0.5 = \pi \, \text{rad/s} $. Centripetal acceleration $ a_c = \omega^2 R = (\pi)^2 \times 1 \approx 9.87 \, \text{m/s}^2 $.

Question 2

A projectile is launched at $ 16 \, \text{m/s} $ at $ 37^\circ $. What is its horizontal velocity component? (Take $ \cos 37^\circ = 0.8 $)

Accepted Answer

Horizontal velocity $ v_x = v_0 \cos \theta_0 $. Given: $ v_0 = 16 \, \text{m/s}, \cos 37^\circ = 0.8 $. $ v_x = 16 \times 0.8 = 12.8 \, \text{m/s} $.

Question 3

For an object in motion with constant acceleration in a plane, what is true when the acceleration is parallel to the initial velocity?

Accepted Answer

When the constant acceleration is parallel to the initial velocity, the motion occurs in a straight line along the direction of the initial velocity, as the acceleration only changes the magnitude of the velocity, not its direction.

NEET Physics: Motion in a Plane — Practice Set 6

Q1. A particle moves in a circular path of radius \( 1 \, \text{m} \) completing 3 revolutions in \( 6 \, \text{s} \). What is its centripetal acceleration?

Q2. A projectile is launched at \( 16 \, \text{m/s} \) at \( 37^\circ \). What is its horizontal velocity component? (Take \( \cos 37^\circ = 0.8 \))

Q3. For an object in motion with constant acceleration in a plane, what is true when the acceleration is parallel to the initial velocity?

Q4. A ball is thrown at \( 24 \, \text{m/s} \) at \( 37^\circ \). What is its vertical velocity at \( t = 1 \, \text{s} \)? (Take \( g = 10 \, \text{m/s}^2, \sin 37^\circ = 0.6 \))

Q5. A particle moves in a circle of radius \( 2.5 \, \text{m} \) with a speed of \( 10 \, \text{m/s} \). What is its centripetal acceleration?

Q6. A particle’s position is given by \( x = 4t^2 - t \) and \( y = 2t + t^2 \) (in meters and seconds). What is its speed at \( t = 1 \, \text{s} \)?

Q7. For a projectile launched from the ground, what is true about its time of ascent and time of descent?

Q8. A projectile launched at \( 15 \, \text{m/s} \) at \( 53^\circ \) reaches a horizontal distance of \( 18 \, \text{m} \). What is the value of \( g \)? (Take \( \sin 53^\circ = 0.8, \cos 53^\circ = 0.6 \))

Q9. A particle starts with velocity \( 6 \hat{i} \, \text{m/s} \) and accelerates at \( (2 \hat{i} + 4 \hat{j}) \, \text{m/s}^2 \). What is its speed after \( 3 \, \text{s} \)?

Q10. For an object in motion with constant acceleration in a plane, what is the shape of its path if the initial velocity is zero?