Question

A trolley of mass $3 \,kg$, as shown In figure, is connected to two identical springs, each of spring constant $600 \,N m^{-1}$. If the trolley is displaced from its equilibrium position by $5\, cm$ and released, the maximum speed of the trolley is

• A. $0.5\,m\,s^{-1}$
• B. $1\,m\,s^{-1}$
• C. $2\,m\,s^{-1}$
• D. $3\,m\,s^{-1}$

Answer 1

Answer: (B)

In the given figure, two identical springs are connected in parallel.
$\therefore $ The effective spring constant is
$k_{eff} = 2k = 2 \times 600 \,N \,m^{- 1} = 1200 \,N\,m^{-1}$
Here, Amplitude, $A = 5 \,cm = 0.05 \,m, m = 3\, kg$
Angular frequency of oscillation
$\omega =\sqrt{\frac{k_{eff}}{m}} = \sqrt{\frac{1200 N m^{-1}}{3 kg}} = 20 s^{-1}$
Maximum speed, $v_{\text{max}}= A \omega$
$ = (0.05 \,m)(20\, s^{-1}) = 1\, m\, s^{-1}$