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A uniform rod AB of length $l$ and mass $m$ is free to rotate about point A. The rod is released from rest in horizontal position. Given that the moment of inertia of the rod about A is $\frac{ml^2}{3}$, the initial angular acceleration of the rod will be:
Which of the following will not be affected if the radius of the sphere is increased while keeping mass constant?
In uniform circular motion:
If rotational kinetic energy is $50\%$ of translational kinetic energy, then the body is:
The increase in the width of the depletion region in a p-n junction diode is due to :
A solid cylinder of mass $50 \text{ kg}$ and radius $0.5 \text{ m}$ is free to rotate about the horizontal axis. A massless string is wound round the cylinder with one end attached to it and other hanging freely. Tension in the string required to produce an angular acceleration of $2 \text{ rev/s}^2$ is:
A rope is wound around a hollow cylinder of mass $3\text{ kg}$ and radius $40\text{ cm}$. What is the angular acceleration of the cylinder, if the rope is pulled with a force of $30\text{ N}$?
A man of $50 \text{ kg}$ mass is standing in a gravity free space at a height of $10 \text{ m}$ above the floor. He throws a stone of $0.5 \text{ kg}$ mass downwards with a speed $2 \text{ m s}^{-1}$. When the stone reaches the floor, the distance of the man above the floor will be:
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 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:
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:
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:
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:
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)
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 :
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: