A system consists of block A and B each of mass m connected by a light spring of spring constant k as shown with block B in contact with a wall- The block A is moved towards B by a distance 3mgk from natural length of spring and then released from rest- Neglect friction anywhere-Acceleration of centre of mass of system comprising A and B just after A is released is-

The correct option is B 3g2 At equilibrium before releasing the block B, x=k(3mgk) After releasing the block A ,its acceleration towards right is a. ...

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Standard XII

Physics

Spring Block's Time Period

A system cons...

Question

A system consists of block A and B each of mass $m$ connected by a light spring of spring constant $k$ as shown with block B in contact with a wall. The block A is moved towards B by a distance $\frac{3 m g}{k}$ from natural length of spring and then released from rest. Neglect friction anywhere.
Acceleration of centre of mass of system comprising A and B just after A is released is:

0

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\frac{3 g}{2}

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3 g

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none of these

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Solution

The correct option is B $\frac{3 g}{2}$
At equilibrium before releasing the block B, $x = k (\frac{3 m g}{k})$
After releasing the block A ,its acceleration towards right is a.
$k x = m a$
$k (\frac{3 m g}{k}) = m a$
$a = 3 g$
Block B will not move,its acceleration =0
Now, acceleration of center of mass is $a_{c o m}$
$a_{c o m} = \frac{m_{A} a + m_{B} 0}{m_{A} + m_{B}} = \frac{m (3 g)}{m + m} = \frac{3 g}{2} m / s^{2}$

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The correct option is B 3g2At equilibrium before releasing the block B, x=k(3mgk)After releasing the block A ,its acceleration towards right is a.kx=mak(3mgk)=maa=3gBlock B will not move,its acceleration =0Now, acceleration of center of mass is acomacom=mAa+mB0mA+mB=m(3g)m+m=3g2m/s2