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The mean free path l for a gas molecule depends upon the diameter, d of the molecule as:
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
The value $\gamma = \frac{C_P}{C_V}$ for hydrogen, helium, and another ideal diatomic gas $X$ (whose molecules are not rigid but have an additional vibrational mode), are respectively equal to:
An object of mass $500 \text{ g}$ initially at rest is acted upon by a variable force whose $x$-component varies with $x$ in the manner shown. The velocities of the object at the points $x=8 \text{ m}$ and $x=12 \text{ m}$ would have the respective values of nearly:
An ideal gas at $0^\circ\text{C}$ and atmospheric pressure $P$ has volume $V$. The percentage increase in its temperature needed to expand it to $3V$ at constant pressure is:
Two sound waves with wavelengths $5.0 \text{ m}$ and $5.5 \text{ m}$, respectively, propagate in a gas with a velocity of $330 \text{ m/s}$. How many beats per second can we expect?
A $100 \text{ g}$ iron ball having velocity $10 \text{ m/s}$ collides with a wall at an angle $30^\circ$ and rebounds with the same angle. If the period of contact between the ball and wall is $0.1 \text{ second}$, then the force experienced by the wall is:
Three vessels of equal capacity have gases at the same temperature and pressure. The first vessel contains helium (monoatomic), the second contains fluorine (diatomic) and the third contains sulfur hexafluoride (polyatomic). The correct statement, among the following, is:
At any instant of time $t$, the displacement of any particle is given by $2t-1$ (SI unit) under the influence of the force of $5\text{ N}$. The value of instantaneous power (in SI units) is:
The temperature at which the RMS speed of atoms in neon gas is equal to the RMS speed of hydrogen molecules at $15^\circ\text{C}$ is: (the atomic mass of neon $= 20.2 \text{ u}$, molecular mass of hydrogen $= 2 \text{ u}$)
The potential energy of a long spring when stretched by $2\text{ cm}$ is $U$. If the spring is stretched by $8\text{ cm}$, the potential energy stored in it will be:
A bomb of $12 \text{ kg}$ explodes into two pieces of masses $4 \text{ kg}$ and $8 \text{ kg}$. The velocity of $8 \text{ kg}$ mass is $6 \text{ m/sec}$. The kinetic energy of the other mass is:
The following graph represents the T-V curves of an ideal gas (where T is the temperature and V the volume) at three pressures $P_1, P_2$ and $P_3$ compared with those of Charles's law represented as dotted lines. Then the correct relation is:
An arrangement of three parallel straight wires placed perpendicular to the plane of paper carry the same current $I$ along the same direction as shown in the figure. The magnitude of force per unit length on the middle wire $B$ is given by:
Given below are two statements: Assertion (A): When a firecracker (rocket) explodes in mid-air, its fragments fly in such a way that they continue moving in the same path, which the firecracker would have followed, had it not exploded. Reason (R): The explosion of cracker (rocket) occurs due to internal forces only and no external force acts for this explosion.
Force $F$ on a particle moving in a straight line varies with distance $d$ as shown in the figure. The work done on the particle during its displacement of $12$ m is:
A block of mass $M$ is attached to the lower end of a vertical spring. The spring is hung from the ceiling and has a force constant value of $k$. The mass is released from rest with the spring initially unstretched. The maximum extension produced along the length of the spring will be:
If a diamagnetic substance is brought near the north or the south pole of a bar magnet, it is
An electric lift with a maximum load of $2000\text{ kg}$ (lift+passengers) is moving up with a constant speed of $1.5\text{ m s}^{-1}$. The frictional force opposing the motion is $3000\text{ N}$. The minimum power delivered by the motor to the lift in watts is: (Take $g=10\text{ m s}^{-2}$)
Three different objects of mass $m_1$, $m_2$ and $m_3$ are allowed to fall from rest and from the same point 'O' along three different frictionless paths. The speeds of the three objects, on reaching the ground, will be in the ratio of: