A body of mass 2 kg moves with velocity of 18 m / s hits a spring fixed at other end of force constant 1000 N / m and comes to rest after compressing the spring. The compression of the springs is

Question

A body of mass 2 kg moves with velocity of 18 m / s hits a spring fixed at other end of force constant 1000 N / m and comes to rest after compressing the spring. The compression of the springs is (A) 0.80 m (B) 0.60 m (C) 0.79 m (D) 0.100 m

Tardigrade Admin · Accepted Answer

Total kinetic energy converted into potential energy (1/2) m v2=(1/2) k x2 √(m v2/k)=x √(2 × 18 × 18/1000)=x ⇒ x=√(648/1000)=(25.45/10 × √10) x =0.80 m

Q. A body of mass $2 k g$ moves with velocity of $18 m / s$ hits a spring fixed at other end of force constant $1000 N / m$ and comes to rest after compressing the spring. The compression of the springs is

$0.80 m$

$0.60 m$

$0.79 m$

$0.100 m$

Total kinetic energy converted into potential energy
$\frac{1}{2} m v^{2} = \frac{1}{2} k x^{2}$
$\frac{m v ^{2}}{k} = x$
$\frac{2 \times 18 \times 18}{1000} = x$
$\Rightarrow x = \frac{648}{1000} = \frac{25.45}{10 \times 10}$
$x = 0.80 m$

Q. A body of mass 2kg moves with velocity of 18m/s hits a spring fixed at other end of force constant 1000N/m and comes to rest after compressing the spring. The compression of the springs is

0.80m

0.60m

0.79m

0.100m