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Two bodies of masses $m_1$ and $m_2$ have equal kinetic energies. If $p_1$ and $p_2$ are their respective momenta, then the ratio $p_1 : p_2$ is equal 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:
Two bodies with kinetic energies in the ratio of $4 : 1$ are moving with equal linear momentum. The ratio of their masses is:
By which method was a new breed 'Hisardale' of sheep formed by using Bikaneri ewes and Marino rams?
The moment of inertia of a uniform circular disc is maximum about an axis perpendicular to the disc and passing through:
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 $30\text{ N}$?
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 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 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?
Phenanthrene is an aromatic compound and follows Hückel's $(4n+2)\pi$ electron rule. The value of $n$ is: