A body of mass 1 kg falls freely from lens of 100 m on a platform of mass 3 kg which is mounted on a spring having spring constant K=1.25×106 N/m. The body sticks to the platform and the spring’s maximum compression is found to be x. Given that g=10ms−2, the value of x will be close to (a) 4 cm (b) 8 cm (c) 80 cm (d) 40 cm

Question ID - 50316 | SaraNextGen Top Answer A body of mass 1 kg falls freely from lens of 100 m on a platform of mass 3 kg which is mounted on a spring having spring constant K=1.25×106 N/m. The body sticks to the platform and the spring’s maximum compression is found to be x. Given that g=10ms−2, the value of x will be close to (a) 4 cm (b) 8 cm (c) 80 cm (d) 40 cm

Answer Key / Explanation : (a) -

Velocity of 1 kg block just before it collides with 3kg block ==m/s

Applying momentum conversation just before and just after collision.

=4v⇒v= m/s

Initial compression of spring

1.25×106x0=30⇒x0≈0

applying work energy theorem,

wg +  wsp=KE

⇒40×x+×1.25×106(02−x2)

=0−×4×v2

Solving x≈ 4 cm