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If $\vec{F}$ is the force acting on a particle having position vector $\vec{r}$ and $\vec{\tau}$ be the torque of this force about the origin, then:
The ratio of the radii of gyration of a circular disc to that of a circular ring, each of the same mass and radius, around their respective axes is:
A sample of $0.1 \text{ g}$ of water at $100^{\circ}\text{C}$ and normal pressure ($1.013 \times 10^5 \text{ N m}^{-2}$) requires $54 \text{ cal}$ of heat energy to convert it into steam at $100^{\circ}\text{C}$. If the volume of the steam produced is $167.1 \text{ cc}$, then the change in internal energy of the sample will be:
A Carnot engine whose sink is at $300 \text{ K}$ has an efficiency of $40\%$. By how much should the temperature of the source be increased to increase its efficiency by $50\%$ of its original efficiency?
Ratio of total kinetic energy and rotational kinetic energy in the motion of a disc is:
Three masses are placed on the x-axis: $300 \text{ g}$ at the origin, $500 \text{ g}$ at $x = 40 \text{ cm}$, and $400 \text{ g}$ at $x = 70 \text{ cm}$. The distance of the center of mass from the origin is:
A black body is at $727^\circ\text{C}$. The rate at which it emits energy is proportional to:
Thermodynamic processes are indicated in the following diagram. Match the following: Column I P. Process I Q. Process II R. Process III S. Process IV Column II a. Adiabatic b. Isobaric c. Isochoric d. Isothermal
Two bodies with kinetic energies in the ratio of $4 : 1$ are moving with equal linear momentum. The ratio of their masses is:
The angular speed of the wheel of a vehicle is increased from $360 \text{ rpm}$ to $1200 \text{ rpm}$ in $14 \text{ seconds}$. Its angular acceleration will be:
An object kept in a large room having an air temperature of $25^\circ \text{C}$ takes $12 \text{ min}$ to cool from $80^\circ \text{C}$ to $70^\circ \text{C}$. The time taken to cool for the same object from $70^\circ \text{C}$ to $60^\circ \text{C}$ would be nearly:
The temperature inside a refrigerator is $t_2^\circ\text{C}$ and the room temperature is $t_1^\circ\text{C}$. The amount of heat delivered to the room for each joule of electrical energy consumed ideally will be:
The ratio of the moments of inertia of two spheres, about their diameters, having the same mass and their radii being in the ratio of $1:2$, is:
The coefficient of linear expansion of brass and steel rods are $\alpha_1$ and $\alpha_2$. Lengths of brass and steel rods are $L_1$ and $L_2$ respectively. If $(L_2-L_1)$ remains the same at all temperatures, which one of the following relations holds good?
If the cold junction of a thermocouple is kept at $0^\circ\text{C}$ and the hot junction is kept at $T^\circ\text{C}$, then the relation between neutral temperature ($T_n$) and temperature of inversion ($T_i$) is:
The molar specific heat at a constant pressure of an ideal gas is $(7/2)R$. The ratio of specific heat at constant pressure to that at constant volume is:
The two ends of a metal rod are maintained at temperatures $100 ^\circ\text{C}$ and $110 ^\circ\text{C}$. The rate of heat flow in the rod is found to be $4.0 \text{ J/s}$. If the ends are maintained at temperatures $200 ^\circ\text{C}$ and $210 ^\circ\text{C}$, the rate of heat flow will be:
The coefficients of linear expansion of brass and steel rods are $\alpha_1$ and $\alpha_2$, lengths of brass and steel rods are $l_1$ and $l_2$ respectively. If $(l_2 - l_1)$ is maintained the same at all temperatures, which one of the following relations holds good?
The internal energy change in a system that has absorbed $2\text{ kcal}$ of heat and done $500\text{ J}$ of work is
A thermodynamic system undergoes a cyclic process $ABCDA$ as shown in Fig. The work done by the system in the cycle is: