A mass of 1 kg moving with a speed of 2 m/s on a . . .

Question : A mass of 1 kg moving with a speed of 2 m/s on a horizontal smooth surface, collides with a nearly weightless spring of force constant k=100 N/m. The maximum compression of the spring would be :

(a) 0.02 m

(b) 0.5 m

(c) 0.2 m

(d) 0.05 m

Doubt by Jaskirat

Solution : 

mass (m) = 1 kg 

speed (v) = 2 m/s

Force constant (k) =100 N/m

As per the law of conservation of energy 

The K.E. of the ball will be converted in to the P.E. of the Spring.

KE=PE

½mv²=½kx²

(mv²)/k=x²
x=√[(mv²)/k]
x=√[(mv²)/k]
x=√[(1×(2)²]/100
x=√(4/100)
x=2/10
x=0.2 m

Hence, (c) 0.2 m, would be the correct option.

Similar Question : 

A mass of 0.5 kg moving with a speed of 1.5 m/s on a horizontal surface collides with a nearly weightless spring of force constant k=50 N/m. The maximum compression of the spring would be : 
(a) 0.15 m
(b) 0.12 m
(c) 1.5 m
(d) 0.5 m