Two springs with negligible masses and force | vedclass

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Question

(D) The two springs are connected in parallel to the block. The effective spring constant $K_{eff}$ is given by $K_{eff} = K_1 + K_2 = 200 + 160 = 360

Vedclass · Accepted Answer

$(A)$ and $(B)$ both.

Vedclass · Answer

(D) The two springs are connected in parallel to the block. The effective spring constant $K_{eff}$ is given by $K_{eff} = K_1 + K_2 = 200 + 160 = 360\, Nm^{-1}$.The angular frequency of oscillation is $\omega = \sqrt{\frac{K_{eff}}{m}} = \sqrt{\frac{360}{10}} = \sqrt{36} = 6\, rad/s$.The period of oscillation is $T = \frac{2\pi}{\omega} = \frac{2\pi}{6} = \frac{\pi}{3} \, s$. Thus,option $(A)$ is correct.The impulse $J$ given to the block provides an initial velocity $v_0$ such that $J = m v_0$. Therefore,$v_0 = \frac{J}{m} = \frac{50}{10} = 5\, ms^{-1}$.Since the block starts from the equilibrium position,the initial velocity is the maximum velocity of the oscillation $(v_{max} = v_0 = 5\, ms^{-1})$. Thus,option $(B)$ is correct.Since both $(A)$ and $(B)$ are correct,the correct option is $(D)$.

Column $I$	Column $II$
$(A)$ The object moves on the $x$-axis under a conservative force such that its speed $v = c_1 \sqrt{c_2 - x^2}$,where $c_1, c_2 > 0$.	$(p)$ The object executes simple harmonic motion.
$(B)$ The object moves on the $x$-axis such that its velocity $v = -kx$,where $k > 0$.	$(q)$ The object does not change its direction.
$(C)$ An object is attached to a spring in an elevator accelerating upwards with constant acceleration $a$. The motion is observed from the elevator.	$(r)$ The kinetic energy of the object keeps on decreasing.
$(D)$ The object is projected vertically upwards with speed $2 \sqrt{GM_e / R_e}$.	$(s)$ The object can change its direction only once.

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