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Consider a thin circular ring (A), a circular disc (B), a hollow cylinder (C) and a solid cylinder (D) of the same radii $R$ and of the same masses. If $I_A$, $I_B$, $I_C$ and $I_D$ are their moments of inertia about the axis shown, then choose the correct answer from the options given below:
If the initial tension on a stretched string is doubled, then the ratio of the initial and final speeds of a transverse wave along the string is:
A particle of mass $m$ and charge $(-q)$ enters the region between the two charged plates initially moving along the x-axis with speed $v_x$ (as shown in the figure). The length of the plate is $L$ and a uniform electric field $E$ is maintained between the plates. The vertical deflection of the particle at the far edge of the plate is:
Liquid oxygen at $50 \text{ K}$ is heated up to $300 \text{ K}$ at a constant pressure of $1 \text{ atm}$. The rate of heating is constant. Which one of the following graphs represents the variation of temperature with time?
A black body at $1227^\circ\text{C}$ emits radiations with maximum intensity at a wavelength of $5000 \text{ \AA}$. If the temperature of the body is increased by $1000^\circ\text{C}$, the maximum intensity will be observed at:
A rigid ball of mass $M$ strikes a rigid wall at $60^{\circ}$ and gets reflected without loss of speed, as shown in the figure. The value of the impulse imparted by the wall on the ball will be:
The force $F$ acting on a particle of mass $m$ is indicated by the force-time graph shown below. The change in momentum of the particle over the time interval from $0$ to $8$ s is:
A rod PQ of mass $M$ and length $L$ is hinged at end P. The rod is kept horizontal by a massless string tied to point Q as shown in the figure. When the string is cut, the initial angular acceleration of the rod is:
Given below are two statements: One is labelled as Assertion (A) and the other is labelled as Reason (R) Assertion (A): Semiconservative replication was experimentally proved by Mathew Meselson and Franklin Stahl (1958) Reason (R): Meselson and Stahl used radioactive isotope 15N and equilibrium density gradient centrifugation technique. In the light of the above statements, choose the correct answer from the options given below:
A solid sphere of mass $m$ and radius $R$ is rotating about its diameter. A solid cylinder of the same mass and same radius is also rotating about its geometrical axis with an angular speed twice that of the sphere. The ratio of their kinetic energies of rotation ($E_{\text{sphere}}/E_{\text{cylinder}}$) will be:
A particle moving with velocity $\vec{v}$ is acted by three forces shown by the vector triangle $PQR$. The velocity of the particle will:
A wheel is subjected to uniform angular acceleration about its axis. Initially, its angular velocity is zero. In the first $2\text{ s}$, it rotates through an angle $\theta_1$. In the next $2\text{ s}$, it rotates through an additional angle $\theta_2$. The ratio of $\frac{\theta_2}{\theta_1}$ is:
Find the torque about the origin when a force of $3\hat{j} \text{ N}$ acts on a particle whose position vector is $2\hat{k} \text{ m}$.
If the acceleration due to gravity at a height 1 km above the earth is similar to a depth d below the surface of the earth, then:
Tritium, a radioactive isotope of hydrogen, emits which of the following particles?
A round disc of moment of inertia $I_2$ about its axis perpendicular to its plane and passing through its center is placed over another disc of moment of inertia $I_1$ rotating with an angular velocity $\omega$ about the same axis. The final angular velocity of the combination of discs is:
The force-time (F – t) curve of a particle executing linear motion is as shown in the figure. The momentum acquired by the particle in the time interval from zero to 8 seconds will be:
The average kinetic energy of a gas molecule can be determined by knowing:
The kinetic energy of one gram molecule of a gas at standard temperature and pressure is: (R = 8.31 J/mol-K)
A heavy uniform chain lies on a horizontal table-top. If the coefficient of friction between the chain and table surface is 0.25, then the maximum fraction of the length of the chain that can hang over one edge of the table is: