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In the figure shown a plate of mass 60 g is at rest and in equilibrium. A particle of mass  is released from height 4.5 mg/k from the plate. The particle sticks to the plate. Neglecting the duration of collision find the time from the collision of the particle and plate to the moment when the spring has maximum compression. Spring has force constant 1 N/m. Calculate the value of time in the form  and find the value of


Question ID - 153906 | SaraNextGen Top Answer

In the figure shown a plate of mass 60 g is at rest and in equilibrium. A particle of mass  is released from height 4.5 mg/k from the plate. The particle sticks to the plate. Neglecting the duration of collision find the time from the collision of the particle and plate to the moment when the spring has maximum compression. Spring has force constant 1 N/m. Calculate the value of time in the form  and find the value of

1 Answer
127 votes
Answer Key / Explanation : (5) -

(5)

Velocity of the particle before collision

Now it collides with the plate

Now just after collision velocity  of the system of ‘plate+ particle’

Now the system performs SHM with time period  and mean position as

Distance below the point of oscillation

Let the equation of motion is

At

From Eqs. (i) and (ii)

From Eqs. (iii) and (iv)

Hence equation of SHM should be

The plate will be at rest again when

Using value,

 

 

 
127 votes

127
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