Question

A block of 4 kg mass starts at rest and slides a distance d down a frictionless incline (angle ${30}^0$) 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 = $10m{s}^{-1}$)

• A. 25 cm
• B. 38.3 cm
• C. 62.5 cm
• D. None of the above

Answer 1

The correct option is B 38.3 cm

we have,

$U=\frac{1}{2}k{x}^2$

$=\frac{1}{2}\times 431\times {0.21}^2$

$=9.5J$

$mgy=U$

$mg(d+x)\sin 30=9.5$

$3.2\times 9.8(d+0.21)\frac{1}{2}=9.5$

solving the above equation, we get,

$d=0.383m$

$\Rightarrow d=38.3cm$