devarshi-dt-logo

Question:

A body of mass 1kg falls freely from a height of 100m on a platform of mass 3kg which is mounted on a spring having spring constant k=1.25x10⁶N/m. The body sticks to the platform and the spring's maximum compression is found to be x. Given that g=10m/s², the value of x will be close to:

4cm

8cm

80cm

None of these

Solution:

The correct option is A 4cm
Initial compression is negligible
Compression will be significant due to collision.
velocity after collision
1 × √2 × 10 × 100 = 4 + v
v = 5√5 m/s
Assuming this as maximum velocity
v = ωA
5√5 = √1.25 × 10⁶ / 4 A
A = 5 × 2 × 2 × 10⁻² m = 2cm