Browse and search thousands of solved questions for your preparation.
Free questions with full explanations — locked behind signup to protect quality.
A black body at $227^\circ\text{C}$ radiates heat at the rate of $7 \text{ cal cm}^{-2}\text{s}^{-1}$. At a temperature of $727^\circ\text{C}$, the rate of heat radiated in the same units will be:
An energy of $484 \text{ J}$ is spent in increasing the speed of a flywheel from $60 \text{ rpm}$ to $360 \text{ rpm}$. The moment of inertia of the flywheel is:
An object flying in the air with velocity $(20\hat{i} + 25\hat{j} - 12\hat{k})$ suddenly breaks into two pieces whose masses are in the ratio of $1:5$. The smaller mass flies off with a velocity $(100\hat{i} + 35\hat{j} + 8\hat{k})$. The velocity of the larger piece will be:
The wavelength of the first spectral line in the Balmer series of hydrogen atom is 6561 Å. The wavelength of the second spectral line in the Balmer series of singly ionized helium atom is:
The position of a particle is given by $\vec{r} = \hat{i} + 2\hat{j} - \hat{k}$ and momentum $\vec{P} = 3\hat{i} + 4\hat{j} - 2\hat{k}$. The angular momentum is perpendicular to:
A hollow sphere of diameter $0.2 \text{ m}$ and mass $2 \text{ kg}$ is rolling on an inclined plane with velocity $v = 0.5 \text{ m/s}$. The kinetic energy of the sphere is:
Match List-I (Spectral Series) with List-II (corresponding wave number expressions). List-I (Series) A. Balmer series B. Lyman series C. Brackett series D. Pfund series List-II (Wave number in cm⁻¹) I. R(1/1² - 1/n²) II. R(1/4² - 1/n²) III. R(1/5² - 1/n²) IV. R(1/2² - 1/n²) Choose the correct answer from the options given below:
A thin circular ring of mass $M$ and radius $r$ is rotating about its axis with a constant angular velocity $\omega$. Four objects each of mass $m$, are kept gently to the opposite ends of two perpendicular diameters of the ring. The angular velocity of the ring will be:
A constant torque of $100\text{ N m}$ turns a wheel of moment of inertia $300\text{ kg m}^2$ about an axis passing through its centre. Starting from rest, its angular velocity after $3\text{ s}$ is:
The distance covered by a body of mass $5 \text{ g}$ having linear momentum $0.3 \text{ kg m/s}$ in $5 \text{ s}$ is:
In the Bohr's model of a hydrogen atom, the centripetal force is furnished by the Coulomb attraction between the proton and the electron. If a₀ is the radius of the ground state orbit, m is the mass and e is the charge on the electron, ε₀ is the vacuum permittivity, the speed of the electron is:
Two discs of same moment of inertia rotating about their regular axis passing through centre and perpendicular to the plane of disc with angular velocities $\omega_1$ and $\omega_2$. They are brought into contact face to face coinciding the axis of rotation. The expression for loss of energy during this process is:
ABC is an equilateral triangle with O as its centre. $\vec{F}_1$, $\vec{F}_2$ and $\vec{F}_3$ represent three forces acting along the sides AB, BC and AC respectively. If the total torque about O is zero then the magnitude of $\vec{F}_3$ is:
A copper rod of $88 \text{ cm}$ and an aluminium rod of an unknown length have an equal increase in their lengths independent of an increase in temperature. The length of the aluminium rod is: ($\alpha_{\text{Cu}} = 1.7 \times 10^{-5} \text{ K}^{-1}$ and $\alpha_{\text{Al}} = 2.2 \times 10^{-5} \text{ K}^{-1}$)
Three identical spheres, each of mass $M$, are placed at the corners of a right-angle triangle with mutually perpendicular sides equal to $2 \text{ m}$ (see figure). Taking the point of intersection of the two mutually perpendicular sides as the origin, find the position vector of the centre of mass.
The moment of inertia of a thin uniform rod of mass $M$ and length $L$ about an axis passing through its mid-point and perpendicular to its length is $I_0$. Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is:
A black body at $227^{\circ}\text{C}$ radiates heat at the rate of $7\text{ cal cm}^{-2}\text{s}^{-1}$. At a temperature of $727^{\circ}\text{C}$, the rate of heat radiated in the same units will be
A particle of mass $m$ is projected with velocity $v$ making an angle of $45^\circ$ with the horizontal. When the particle lands on the level ground, the magnitude of the change in its momentum will be:
A shell of mass $m$ is at rest initially. It explodes into three fragments having masses in the ratio $2:2:1$. If the fragments having equal masses fly off along mutually perpendicular directions with speed $v$, the speed of the third (lighter) fragment is:
It is easier to draw up a wooden block along a smooth inclined plane than to haul it vertically, principally because: