A mass of 0.5 kg moving with a speed of 1.5 m/s on a horizontal smooth surface, collides with a nearly weightless spring of force constant k = 50 N/m. The maximum compression of the spring would be :

Question

A mass of 0.5 kg moving with a speed of 1.5 m/s on a horizontal smooth 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

Tardigrade Admin · Accepted Answer

By the law of conservation of energy, kinetic energy of mass = energy stored in spring i.e., (1/2)mv2=(1/2)kx2 ∴ x2=(mv2/k) ⇒ x=√( . (mv2/k) ) . ⇒ x=√( (0.5× 1.5× 1.5/50) ) So, x=0.15 m

Q. A mass of $0.5 k g$ moving with a speed of $1.5 m / s$ on a horizontal smooth surface, collides with a nearly weightless spring of force constant $k = 50 N / m$ . The maximum compression of the spring would be :

0.15 m

0.12 m

1.5 m

0.5 m

By the law of conservation of energy,
kinetic energy of mass = energy stored in spring
i.e., $\frac{1}{2} m v^{2} = \frac{1}{2} k x^{2}$
$∴$ $x^{2} = \frac{m v ^{2}}{k}$
$\Rightarrow$ $x = (\frac{m v ^{2}}{k})$
$\Rightarrow$ $x = (\frac{0.5 \times 1.5 \times 1.5}{50})$
So, $x = 0.15 m$

Q. A mass of 0.5kg moving with a speed of 1.5m/s on a horizontal smooth surface, collides with a nearly weightless spring of force constant k=50N/m. The maximum compression of the spring would be :