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

The kinetic energy of mass is converted into energy required to compress a spring which is given by ⇒ (1/2) m v2=(1/2) k x2 ⇒ dotx=√(m v2/k) =√(0.5 ×(1.5)2/50)=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

The kinetic energy of mass is converted into energy required to compress a spring which is given by
$\Rightarrow \frac{1}{2} m v^{2} = \frac{1}{2} k x^{2}$
$\Rightarrow \overset{x}{˙} = \frac{m v ^{2}}{k}$
$= \frac{0.5 \times ( 1.5 ) ^{2}}{50} = 0.15 m$

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