A block of rectangular size of mass $$m$$ and area of cross-section $$A$$, floats in a liquid of density $$\rho$$. If we give a small vertical displacement from equilibrium, it undergoes SHM with time period $$T$$, then

Assertion A pendulum is falling freely its time period becomes zero.

Reason Freely falling body has the acceleration equal to g.

A load of mass $m$ falls from a height $$h$$ on the scale pan hung from a spring as shown. If the spring constant is $$k$$ and mass of the scale pan is zero and the mass $$m$$ does not bounce relative to the pan, then the amplitude of vibration is

Assertion : A spring of force constant $k$ is cut into two pieces having lengths in the ratio 1 : 2. The force constant of series combination of the two parts is $$\frac{3 k}{2}$$.

Reason : The spring connected in series are represented by $$k=k_1+k_2$$