Conservation of Energy

Q. The string of a pendulum is attached to a bob and is released from its initial rest position. A fixed peg is present in the path of motion of the pendulum. What are the velocities of the bob at positions $B$ and $C$ respectively? The distances are as shown in the figure.

1. $3.16\text{m/s}$ and $7.07\text{m/s}$
2. $7.07\text{m/s}$ and $3.16\text{m/s}$
3. $5.34\text{m/s}$ and $10.78\text{m/s}$
4. $7.07\text{m/s}$ and $6.32\text{m/s}$

Q. How much energy must a gamma ray photon have, if it is to materialize into a pair of electron and positron, with each particle having a $K.E$ of $1\text{MeV}$?

1. $1.0\text{MeV}$
2. $2\text{MeV}$
3. $3.02\text{MeV}$
4. $0.5\text{MeV}$

Q. How much energy must a gamma ray photon have, if it is to materialize into a pair of electron and positron, with each particle having a $K.E$ of $1\text{MeV}$?

1. $0.5\text{MeV}$
2. $1.0\text{MeV}$
3. $2\text{MeV}$
4. $3.02\text{MeV}$

Q. A motor cycle engine delivers a power of $10\text{kW}$ by consuming petrol at the rate of $2.4\text{kg/hr}$. Find the rate of heat rejection by the exhaust, if the calorific value of petrol is $35.5\text{MJ/kg}$.
(Neglect the other losses)

1. $13.7\text{kW}$
2. $23.7\text{kW}$
3. $33.7\text{kW}$
4. $13.7\text{W}$

Q.

The A and B are two systems whose interaction with surroundings are as shown above, which of the following options correctly characterise the systems A and B.

1. Open system, Closed system
2. Isolated system, Closed system
3. Adiabatic system, Isolated system
4. Closed system, Isolated system

Q. A motor cycle engine delivers a power of $10\text{kW}$ by consuming petrol at the rate of $2.4\text{kg/hr}$. Find the rate of heat rejection by the exhaust, if the calorific value of petrol is $35.5\text{MJ/kg}$.
(Neglect the other losses)

1. $13.7\text{kW}$
2. $23.7\text{kW}$
3. $33.7\text{kW}$
4. $13.7\text{W}$

Q. A simple pendulum consists of a bob of mass $m$ and a light string of length $l$ as shown in the figure. Another identical ball moving with a small velocity $v_0$ collides with the pendulum's bob and sticks to it. For this new pendulum of mass $2m$, which of the following statement(s) is/are correct ?

1. Time period of the pendulum is $2\pi \sqrt{\frac{l}{g}}$.
2. The equation of motion for this pendulum is $\theta =\frac{v_0}{2\sqrt{gL}}\sin \left[\sqrt{\frac{g}{l}}t\right]$.
3. The equation of motion for this pendulum is $\theta =\frac{v_0}{4\sqrt{gl}}\cos \left[\sqrt{\frac{g}{l}}t\right]$.
4. Time period of the pendulum is $2\pi \sqrt{\frac{2l}{g}}$.

Q. The bob of a simple pendulum is displaced from its equilibrium position $O$ to a position $Q$, which is at height $h$ above $O$ and the bob is then released. Assuming the mass of the bob to be $m$ and time period of oscillations to be $2\text{s}$, the tension in the string, when the bob passes through $O$ is

1. $m(g+\pi \sqrt{2gh})$
2. $m(g+\sqrt{{\pi }^{2}gh})$
3. $m(g+\sqrt{\frac{\pi }{2}gh})$
4. $m(g+\sqrt{\frac{{\pi }^2}{3}}gh)$