Question

A toy cork gun contains a spring whose spring constant is 10.0 N/m.
The spring is compressed 5 cm and then used to propel a 6.00 g cork.
The cork, however, sticks to the spring for 1.00 cm beyond its
unstretched length before separation occurs. The muzzle velocity of
this cork is:
(A) 1.02 m/s (B) 1.41 m/s (C) 2.00 m/s
(D)
2.04 m/s
m​

Answer 1

applying law of conservation of energy,

initial spring potential energy = final spring potential energy + kinetic energy of cork

⇒1/2 kx² = 1/2 kx'² + 1/2 mv²

⇒kx² = kx'² = mv²

here , k = 10N/m

x = 5cm = 0.05 m

x' = 1cm = 0.01 m

m = 6g = 0.006 kg

now, 10(0.05)² = 10(0.01)² + 0.006v²

⇒10 × 25 × 10^-4 = 10 × 10^-4 + 0.006 v²

⇒250 × 10^-1 = 10 × 10^-1 + 6v²

⇒25 - 1 = 6v²

⇒v² = 24/6 = 4

⇒v = 2 m/s

hence, option (C) is correct choice.

Answer 2

$\huge\bold\purple{Answer:-}$

initial spring potential energy = final spring potential energy + kinetic energy of cork

⇒1/2 kx² = 1/2 kx'² + 1/2 mv²

⇒kx² = kx'² = mv²

here , k = 10N/m

x = 5cm = 0.05 m

x' = 1cm = 0.01 m

m = 6g = 0.006 kg

now, 10(0.05)² = 10(0.01)² + 0.006v²

⇒10 × 25 × 10^-4 = 10 × 10^-4 + 0.006 v²

⇒250 × 10^-1 = 10 × 10^-1 + 6v²

⇒25 - 1 = 6v²

⇒v² = 24/6 = 4

⇒v = 2 m/s