Two simple pendulums having lengths $l_1$ and $l_2$ with negligible string mass undergo angular displacements $\theta_1$ and $\theta_2$, from their mean positions, respectively. If the angular accelerations of both pendulums are same, then which expression is correct?

Two blocks of masses $m$ and $M,(M>m)$, are placed on a frictionless table as shown in figure. A massless spring with spring constant k is attached with the lower block. If the system is slightly displaced and released, then ( $\mu=$ coefficient of friction between the two blocks)

A. The time period of small oscillation of the two blocks is $T=2 \pi \sqrt{\frac{(m+M)}{k}}$

B. The acceleration of the blocks is $a=-\frac{k x}{M+m}$ ( $x=$ displacement of the blocks from the mean position)

C. The magnitude of the frictional force on the upper block is $\frac{m \mu|x|}{M+m}$

D. The maximum amplitude of the upper block, if it does not slip, is $\frac{\mu(M+m) g}{k}$

E. Maximum frictional force can be $\mu(\mathrm{M}+\mathrm{m}) \mathrm{g}$.

Choose the correct answer from the options given below :

A particle is subjected to two simple harmonic motions as : $$ x_1=\sqrt{7} \sin 5 \mathrm{tcm} $$ and $x_2=2 \sqrt{7} \sin \left(5 t+\frac{\pi}{3}\right) \mathrm{cm}$ where $x$ is displacement and $t$ is time in seconds. The maximum acceleration of the particle is $x \times 10^{-2} \mathrm{~ms}^{-2}$. The value of $x$ is :

Two bodies A and B of equal mass are suspended from two massless springs of spring constant k₁ and k₂, respectively. If the bodies oscillate vertically such that their amplitudes are equal, the ratio of the maximum velocity of A to the maximum velocity of B is