Browse and search thousands of solved questions for your preparation.
Free questions with full explanations — locked behind signup to protect quality.
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 angular speed of a flywheel moving with uniform angular acceleration changes from $1200 \text{ rpm}$ to $3120 \text{ rpm}$ in $16 \text{ s}$. The angular acceleration in $\text{rad/s}^2$ 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:
The ratio of the radius of gyration of a solid sphere of mass $M$ and radius $R$ about its own axis to the radius of gyration of the thin hollow sphere of the same mass and radius about its axis is:
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 moment of the force, $\vec{F} = 4\hat{i} + 5\hat{j} - 6\hat{k}$ at point $(2, 0, -3)$ about the point $(2, -2, -2)$ is given by:
A wheel of a bullock cart is rolling on a level road as shown in the figure below. If its linear speed is $v$ in the direction shown, which one of the following options is correct ($P$ and $Q$ are any highest and lowest points on the wheel, respectively)?
The ratio of the radius of gyration of a thin uniform disc about an axis passing through its centre and normal to its plane to the radius of gyration of the disc about its diameter 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?
Two rods $A$ and $B$ of different materials are welded together as shown in the figure. Their thermal conductivities are $K_1$ and $K_2$. The thermal conductivity of the composite rod will be:
A black body is at a temperature of $5760 \text{ K}$. The energy of radiation emitted by the body at wavelength $250 \text{ nm}$ is $U_1$, at wavelength $500 \text{ nm}$ is $U_2$ and that at $1000 \text{ nm}$ is $U_3$. Wien's constant, $b = 2.88 \times 10^6 \text{ nm K}$. Which of the following is correct?
The value of the coefficient of volume expansion of glycerine is $5 \times 10^{-4} \text{ K}^{-1}$. The fractional change in the density of glycerine for a rise of $40^\circ\text{C}$ in its temperature 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:
On observing light from three different stars $P$, $Q$, and $R$, it was found that the intensity of the violet colour is maximum in the spectrum of $P$, the intensity of the green colour is maximum in the spectrum of $R$ and the intensity of the red colour is maximum in the spectrum of $Q$. If $T_P$, $T_Q$, and $T_R$ are the respective absolute temperatures of $P$, $Q$, and $R$, then it can be concluded from the above observations that:
A black body is at $727^\circ\text{C}$. The rate at which it emits energy is proportional to:
Assuming the sun to have a spherical outer surface of radius $r$, radiating like a black body at temperature $t^\circ \text{C}$, the power received by a unit surface of the earth (normal to the incident rays) at a distance $R$ from the centre of the sun will be: (where $\sigma$ is Stefan's constant)
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:
A $40 \text{ \mu F}$ capacitor is connected to a $200 \text{ V}$, $50 \text{ Hz}$ ac supply. The rms value of the current in the circuit is, nearly :
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:
A deep rectangular pond of surface area $A$, containing water (density = $\rho$, specific heat capacity = $s$), is located in a region where the outside air temperature is at a steady value of $-26^\circ\text{C}$. The thickness of the ice layer in this pond at a certain instant is $x$. Taking the thermal conductivity of ice as $k$, and its specific latent heat of fusion as $L$, the rate of increase of the thickness of the ice layer, at this instant, would be given by: