Exercises

A system of two identical rods ($L$-shaped) of mass $m$ and length $l$ are resting on a peg $P$ as shown in the figure. It the system is displaced in its plane by a small angle $\theta$, find the period of oscillations

The velocity $v$ of a particle of mass $m$ moving along a straight line changes with time $t$ as $\frac{{\mathrm{d}}^{2}v}{\mathrm{d}{t}^2}=-Kv$, where $K$ is a positive constant. Which of the following statement is correct:
 

Two blocks connected by a spring rest on a smooth horizontal plane as shown in the given figure. A constant force $F$ starts acting on block $m_2$ as shown in the figure. Which of the following statements are not correct?

A block of mass $m$ is suspended by a rubber cord of natural length $l=m g / k$, where $k$ is force constant of the cord. The block is lifted upwards so that the cord becomes just tight and then block is released suddenly. Which of the following will not be true?

A cylindrical block of density $d$ stays fully immersed in a beaker filled with two immiscible liquids of different densities $d_1$ and $d_2.$ The block is in equilibrium with half of it in liquid $1$ and the other half in liquid $2$ as shown in the given figure. If the block is given a displacement downwards and released, then neglecting friction study the following statements.

A mass of $0.2\mathrm{kg}$ is attached to the lower end of massless spring of force-constant $200 \mathrm{N} {\mathrm{m}}^{-1}$, the upper end of which is fixed to a rigid support. Which of the following statement is/are true?

A spring of spring constant $k$ stores $5 \mathrm{J}$ of energy when stretched by $25 \mathrm{cm}.$ It is kept vertical with one end fixed. A mass $m$ is attached to the other end. It makes $5$ oscillations per second. Then

Three simple harmonic motions in the same direction, each of amplitude $\text{'}a\text{'}$' and periodic time $\text{'}T\text{'},$ are superimposed. The first and second, and the second and third differ in phase from each other by $\pi /4,$ with the first and third not being identical. Then