Question

A mass of $5\, kg$ is connected to a spring. The potential energy curve of the simple harmonic motion executed by the system is shown in the figure. A simple pendulum of length $4\, m$ has the same period of oscillation as the spring system. What is the value of acceleration due to gravity on the planet where these experiments are performed?

• A. $10 \, m / s ^{2}$
• B. $5 \, m / s ^{2}$
• C. $4 \,m / s ^{2}$
• D. $9.8 \,m / s ^{2}$

Answer 1

Answer: (C)

From potential energy curve
$U _{\max }=\frac{1}{2} kA ^{2} $
$\Rightarrow 10=\frac{1}{2} k (2)^{2}$
$\Rightarrow k =5$
Now $T _{\text {spring }}= T _{\text {pendulum }}$
$2 \pi \sqrt{\frac{5}{5}}=2 \pi \sqrt{\frac{4}{ g }}$
$\Rightarrow 1=\sqrt{\frac{4}{ g }} $
$\Rightarrow g =4$ on planet