Question

A body of mass $1\, kg$ falls freely from a height of $100\, m$ on a platform of mass $3\, kg$ which is mounted on a spring having spring constant $k = 1.25 \times 10^6 \; N/m$. The body sticks to the platform and the spring's maximum compression is found to be $x$. Given that $g = 10 \; ms^{-2}$, the value of $x$ will be close to :

• A. 4 cm
• B. 8 cm
• C. 80 cm
• D. 40 cm

Answer 1

Answer: (A)

4 cm

Answer 2

Velocity of $1\, kg$ block just before it collides with $3\,kg$ block $= \sqrt{2gh} = \sqrt{2000} m/s$
Applying momentum conversation just before and just after collision.
$1 \times \sqrt{2000} = 4 v \; \Rightarrow \; v = \frac{\sqrt{2000}}{4} m /s$
initial compression of spring
$1.25 \times 10^6 \; x_0 = 30 \; \Rightarrow x_0 \approx 0$
applying work energy theorem,
$W_g + W_{sp} = \Delta KE$
$\Rightarrow 40 \times x + \frac{1}{2} \times1.25 \times10^{6} \left(0^{2} -x^{2}\right)$
$= 0 - \frac{1}{2} \times4 \times v^{2}$
solving $x \approx 4 \, cm$