Question

A 1kg mass is attached to a spring of force constant 600N m⁻1 and rests on a smooth horizontal surface with other end of the spring tied to a wall as shown in the figure. A second mass of 0.5kg slides along the surface with initial speed 3m s⁻1. If the masses make a perfectly inelastic collision, then find the amplitude and time period of oscillation of the combined mass. 

• A. \(5\,\text{cm},\,\dfrac{\pi}{10}\,\text{s}\)
• B. \(5\,\text{cm},\,\dfrac{\pi}{5}\,\text{s}\)
• C. \(4\,\text{cm},\,\dfrac{2\pi}{5}\,\text{s}\)
• D. 4cm,(π)/(3)s

Hint:

After inelastic collision, use conservation of momentum before SHM relations.

Answer 1

The Correct Option is B

Step 1: Velocity after perfectly inelastic collision: v=((0.5)(3))/(1+0.5)=1m s⁻1
Step 2: Combined mass: M=1.5kg
Step 3: Angular frequency: ω=√((k)/(M))=√((600)/(1.5))=20rad s⁻1
Step 4: Amplitude: A=(v)/(ω)=(1)/(20)=0.05m=5cm
Step 5: Time period: T=(2π)/(ω)=(π)/(5)s