A body is of mass 1 kg falls freely from a height of 100 m. on a platform of mass 3 kg which is mounted on a spring having spring constant `k=1.25 xx 10 ^6 N//m`.The body sticks to the platform and the spring's maximum compression is found to be x .Given that `g=10 ms ^-2` ,the value of x will be calose to :

Options

A. 40cm
B. 8cm
C. 4cm
D. 80cm

Answer

None

Explanation

Speed of body just before collision:
`u=sqrt(2xx10xx100)=20sqrt(5m//s)`
just after collision `v=u/4=sqrt(5)//s`
By conservation of energy:
`1/2mv^(2)mgx_(1)=1/2(x_(0)+x_(1))^(2)-1/2kxunderset(0)overset(2)`
here `x_(0)` and soving, gives x=2cm