Question

A block of 4 kg mass starts at rest and slides a distance d down a friction less incline (angle ${30}^{\circ }$) where it runs into a spring of negligible mass. The block slides an additional 25 cm before it is brought to rest momentarily by compressing the spring. The force constant of the spring is $400N{m}^{-1}$. The value of d is (take $g=10m{s}^{-2}$)

• A. 25 cm
• B. 37.5 cm
• C. 62.5 cm
• D. None of the above

Answer 1

The correct option is B

37.5 cm

Work done by gravity = change in potential energy of spring

$W_{gravity}=\Delta U_{spring}$

$\left(mgsin\theta \right)(d+0.25)=\frac{1}{2}k(0.25{)}^2$

$d=37.5cm$