$Assertion :$ The time-period of pendulum, on a satellite orbiting the earth is infinity.
$Reason :$ Time-period of a pendulum is inversely proportional to $\sqrt g$

Two springs of constant ${k_1}$and ${k_2}$are joined in series. The effective spring constant of the combination is given by

A body of mass $0.01 kg$ executes simple harmonic motion $(S.H.M.)$ about $x = 0$ under the influence of a force shown below : The period of the $S.H.M.$ is …. $s$

A block with mass $M$ is connected by a massless spring with stiffiess constant $k$ to a rigid wall and moves without friction on a horizontal surface. The block oscillates with small amplitude $A$ about an equilibrium position $x_0$. Consider two cases: ($i$) when the block is at $x_0$; and ($ii$) when the block is at $x=x_0+A$. In both the cases, a perticle with mass $m$ is placed on the mass $M$ ?

($A$) The amplitude of oscillation in the first case changes by a factor of $\sqrt{\frac{M}{m+M}}$, whereas in the second case it remains unchanged

($B$) The final time period of oscillation in both the cases is same

($C$) The total energy decreases in both the cases

($D$) The instantaneous speed at $x_0$ of the combined masses decreases in both the cases

In the following questions, match column $-I$ with column $-II$ and choose the correct options