A body of mass 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=5 N / m . The maximum compression of the spring would be

Question

A body of mass 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=5 N / m . The maximum compression of the spring would be (A) 0.5 m (B) 0.15 m (C) 1.5 m (D) 0.12 m

Tardigrade Admin · Accepted Answer

At maximum compression the whole kinetic energy of ball = potential energy of spring. (1/2)mv2 = (1/2)kx2 ⇒ x = v√(m/k) x = 1.5×√(5/5) = 1.5 m

Q. A body of mass $5 k g$ moving with a speed of $1.5 m / s$ on a horizontal smooth surface collides with a nearly weightless spring of force constant $k = 5 N / m .$ The maximum compression of the spring would be

0.5 m

0.15 m

1.5 m

0.12 m

At maximum compression the whole kinetic energy of ball = potential energy of spring.
$\frac{1}{2} m v^{2} = \frac{1}{2} k x^{2}$
$\Rightarrow x = v \frac{m}{k}$
$x = 1.5 \times \frac{5}{5} = 1.5 m$

Q. A body of mass 5kg moving with a speed of 1.5m/s on a horizontal smooth surface collides with a nearly weightless spring of force constant k=5N/m. The maximum compression of the spring would be