Question

A heavy particle is suspended by a string of length I from a fixed point O. The particle is given a horizontal velocity vₒ. The string slacks at some angle and the particle proceeds on a projectile path. Find the value of vₒ if the particle passes through the point of suspension.

A 5.77 m/s
B 8 m/s
C 9 m/s
D 77 m/s

Answer 1

To find the value of vₒ, we use the concept of projectile motion. When the particle passes through the point of suspension, its velocity will be directed horizontally. The value of vₒ is equal to the horizontal velocity, which is option A) 5.77 m/s.

Step-by-step explanation:

To find the value of vₒ, we can use the concept of projectile motion. When the heavy particle passes through the point of suspension, its velocity will be directed horizontally. At this point, the tension in the string will be zero and the particle will be in free fall. The vertical component of its velocity will be equal to the gravitational acceleration. By using trigonometry, we can calculate the horizontal component of the velocity:

vₓ = vₒ cosθ

where θ is the angle of the string when it slacks. Since the particle passes through the point of suspension, the angle will be 0°. Therefore, the horizontal component of the velocity will be:

vₓ = vₒ

So, the value of vₒ is equal to the horizontal velocity, which is the answer option A) 5.77 m/s.