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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.
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:
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 $g=10\text{ m s}^{-2}$)
The energy that will be ideally radiated by a $100\text{ kW}$ transmitter in $1\text{ hr}$ is:
A thin diamagnetic rod is placed vertically between the poles of an electromagnet. When the current in the electromagnet is switched on, then the diamagnetic rod is pushed up, out of the horizontal magnetic field. Hence the rod gains gravitational potential energy. The work required to do this comes from:
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:
The magnetic susceptibility is negative for
A bullet of mass $m$ hits a stationary block of mass $M$ elastically. The transfer of energy is the maximum, when:
There are four light-weight-rod samples A, B, C, D separately suspended by threads. A bar magnet is slowly brought near each sample and the following observations are noted: (i) A is feebly repelled (ii) B is feebly attracted (iii) C is strongly attracted (iv) D remains unaffected Which one of the following is true?
A vibration magnetometer placed in a magnetic meridian has a small bar magnet. The magnet executes oscillations with a time period of 2 s in earth's horizontal magnetic field of $24\ \mu\text{T}$. When a horizontal field of $18\ \mu\text{T}$ is produced opposite to the earth's field by placing a current-carrying wire, the new time period of the magnet will be:
The venturi-meter works on:
The magnetic moment of a diamagnetic atom is:
The best suited curve showing the variations of susceptibility ($\chi$) of a paramagnetic material in free space with temperature ($T$) is:
A bar magnet is hung by a thin cotton thread in a uniform horizontal magnetic field and is in the equilibrium state. The energy required to rotate it by $60^\circ$ is $W$. Now the torque required to keep the magnet in this new position is:
Curie temperature is the temperature above which:
Two similar springs $P$ and $Q$ have spring constants $k_P$ and $k_Q$, such that $k_P > k_Q$. They are stretched, first by the same amount (case a), then by the same force (case b). The work done by the springs $W_P$ and $W_Q$ are related as, in case (a) and case (b), respectively: