Explore topic-wise InterviewSolutions in Current Affairs.

The total energy of the body executing S.H.M. is E. Then the kinetic energy when the displacement is half of the amplitude, is

[RPMT 1994, 96; CBSE PMT 1995; JIPMER 2002]

The circuit involves two ideal cells connected to a $1\mu F$ capacitor via a key $K$. Initially the key $K$ is in position $1$ and the capacitor is charged fully by $2V$ cell. The key is pushed to position $2$. Column I gives physical quantities involving the circuit after the key is pushed from position $1$ to position $2$. Column II gives corresponding results. Match the statements in Column I with the corresponding values in column II.



$$\begin{array}{cc}\text{Column I}& \text{Column II}\\ \text{(A) The net charge crossing the 4 volt cell in}\mu C\text{is}& \text{(p) 2}\\ \text{(B) The magnitude of work done by 4 volt cell in}\mu J\text{is}& \text{(q) 6}\\ \text{(C) The gain in potential energy of capacitor in}\mu J\text{is}& \text{(r) 8}\\ \text{(D) The net heat produced in}\mu J\text{is}& \text{(s) 16}\end{array}$$

A person is holding a bucket by applying a force of $10N$. He moves a horizontal distance of $5m$ and then climbs up a vertical distance of $10m$. The total work done by him is equal to

A bullet of mass a and velocity b is fired into a large block of mass c. The final velocity of the system is

The frequency of a wave of light is $12\times {10}^{14}{S}^{-1}$ The wave number associated with this light is

An electron in a hydrogen atom undergoes a transition from an orbit with quantum number $n_i$ to another with quantum number $n_f$. $V_i$ and $V_f$ are respectively the initial and final potential energies of the electron. If $\frac{V_f}{V_i}=6.25$, then the smallest possible $n_f$ is

Sinusoidal waves 5.00 cm in amplitude are to be transmitted along a string having a linear mass density equal to $4.00\times {10}^{-2}kg/m$. If the source can deliver a maximum power of 90 W and the string is under a tension of 100 N, then the highest frequency at which the source can operate it, is $(take{\pi }^2=10)$

The energy of a photon in Joules that has a wavelength of 9.0 m is:

A cylinder of mass 5 kg and radius 4 m is rolling purely on a horizontal surface. What will be the angular momentum of the cylinder with respect to any point on the ground if its centre of mass moves with the velocity of 20 m/s?

A block of mass $1\text{kg}$ is at rest relative to a smooth wedge moving leftwards with constant acceleration $a=5{\text{m/s}}^2$

Let $N$ be the normal reaction between the block and the wedge. Then $(g=10{\text{m/s}}^2)$

If the above capacitor is connected across a 6.0 V battery, find (a) the charge supplied by the battery, (b) the induced charge on the dielectric and (c) the net charge appearing on one of the coated surfaces.

The capillaries shown in figure. have inner raii 0.5 mm, 1.0 mm and 1.5 mm respectively. The liquid in the beaker is water. Find the heights of water level in the capillaries. The surface tension of water is $7.5\times {10}^{-2}N{m}^{-1}$.

A particle falls from a height h on a fixed horizontal plate and rebounds. If e is the coefficient of restitution, the total distance travelled by the particle before it stops rebounding is

The maximum range of a gun on horizontal terrain is 16 km. If g = 10m/$s^2$. What must be the muzzle velocity of the shell

Two particles $A$ and $B$ are located at coordinates $(20,0)\text{m}$ and $(30,0)\text{m}$. Relative position of $A$ w.r.t. $B$ is

Two condensers $C_{1}and{C}_2$ are connected in parallel with a battery of constant potential difference and the energies stored in them are found to be in the ratio 1 : 2. If the same condensers were now connected in series with the same battery, the ratio of the potential differences across them will be

A particle $P$ is sliding down a frictionless hemispherical bowl. It passes the point $A$ at $t=0$. At this instant of time, the horizontal component of its velocity is $v$. A bead $Q$ of the same mass as $P$ is ejected from $A$ at $t=0$ along the horizontal string $AB$, with the speed $v$. Friction between the bead and the string may be neglected. Let $t_P$ and $t_Q$ be the respective times taken by $P$ and $Q$ to reach the point $B$. Then:

An $\propto$ particle is situated in an electric field of ${10}^{6}N/C$. The force exerted on it is

The magnetic field due to earth has a vertical component of $30\mu T$ at a place where dip angle is $30°$. Find magnetic field at the point.

A body floats in a liquid contained in a beaker. The whole system as shown falls freely under gravity. The upthrust on the body due to the liquid is

A steel wire of diameter d, area of cross-section A and length 2L is clamped firmly at two points A and B which are 2L metre apart and in the same plane. A body of mass m is hung from the middle point of wire such that the middle point sags by x lower from original position. If Young’s modulus is Y then m is given by

A is singing a note and at the same time B is singing a note with exactly one-eighth the frequency of the note of A. The energies of two sounds are equal, the amplitude of the note of B is

A man of mass 100 kg stands at the rim of a turntable of radius 2m and moment of inertia 4000$kg-m^2$ mounted on a vertical frictionless shaft at its center. The whole system is initially at rest. The man now walks along the outer edge of a turntable with a velocity of 1 m/s relative to the earth. With what angular velocity and in what direction does the turntable rotates?

A hot air balloon is rising vertically upwards at a constant velocity of $10{\text{ms}}^{-1}$. When it is at a height of $45\text{m}$ from the ground, a man bails out from it. After $3\text{s}$ he opens his parachute and decelerates at a constant rate of $5{\text{ms}}^{-2}$. How far is parachutist from the balloon at $t=3\text{s}$?

The coordinates of a moving particle at any time are given by $x=a{t}^2$ and $y=b{t}^2$. The speed of the particle at any moment is

A solid sphere is in rolling motion. In rolling motion a body possesses translational kinetic energy ($K_t$) as well as rotational kinetic energy ($K_r$) simultaneously. The ratio $K_t:(K_t+K_r)$ for the sphere is

The range of a particle when launched at an angle of ${15}^{\circ }$ with the horizontal is 1.5 km. What is the range of the projectile when launched at an angle of ${45}^{\circ }$ to the horizontal

What is the relation between specific conductance (k) and cell constant (G*)

Standing wave is produced in $10\text{m}$ long stretched string. If the string vibrates in $5$ segments and wave velocity is $20\text{m/s}$, then frequency of oscillation is

Two particles $A$ and $B$ initially separated by distance $X$ are projected simultaneously in the directions shown in figure with speed $v_A=20\text{m/s}$ and $v_B=10\text{m/s}$ respectively. They collide in air after $\frac{1}{2}\text{s}.$ Find the distance $X$.

A toy train moves due north at a constant speed 2 m/s along a straight track which is parallel to the wall of a room. The wall is to the east of the track at a distance 4m. There is a toy dart gun on the train with its barrel fixed in a plane perpendicular to the motion of the train. The gun points at an angle ${60}^{\circ }$ to the horizontal. There is a vertical line drawn on the wall, stretching from floor to ceiling, and the dart gun is fired at the instant when the line is due east of the gun. If the dart leaves the gun at speed 8 m/s relative to the gun, find the distance by which the dart misses the vertical line. That is, find how far north or south of the vertical line is the point at which the dart hits the wall.

A particle of mass 1 Kg and carrying 0.01 C is at rest on an inclined plane of angle ${30}^{\circ }$ with horizontal when an electric field of $\frac{490}{\sqrt{3}}N{C}^{-1}$ applied parallel to horizontal, the coefficient of friction is

A thin glass rod is bent into a semicircle of radius r. A charge +Q is uniformly distributed along the upper half and a charge –Q is uniformly distributed along the lower half, as shown in the figure Calculate the electric field E at P, the centre of semicircle.

A particle executes simple harmonic motion with an amplitude of 10 cm. At what distance from the mean position are the kinetic and potential energies equal ?

Two blocks of masses 10 kg and 30 kg are placed along a vertical line.The first block is raised through a height of 7 cm.By what distance should the second mass be moved to raise the centre of mass by 1 cm ?

One end of a spring of natural length h and spring constant k is fixed at the ground and the other is fitted with a smooth ring of mass m which is allowed to slide on a horizontal rod fixed at a height h (figure). Initially, the spring makes an angle of ${37}^{\circ }$ with the vertical when the system is released from rest. Find the speed of the ring when the spring becomes vertical.

A right circular cone of density $\rho ,$ floats just immersed with its vertex downwards, in a vessel containing two liquids of densities ${\sigma }_1$ and ${\sigma }_2$ respectively. The plane of separation of the two liquids cuts off from the axis of the cone at a fraction $z$ (taken from vertex) of its length. Find $z$.

A sphere of radius $R$ has charge density per unit volume, $\rho \left(r\right)=A(R-r),$ for $0<r<R$ ( Here $A$ is constant). If total electric charge inside the sphere is $Q$, then the value of $A$ in terms of $Q$ and $R$ is

A tuning fork of frequency 480 Hz is used to vibrate a sono-meter wire having natural frequency 240 Hz. The wire will vibrate with a frequency of

Two forces $\overrightarrow{F_1}=(2\hat{i}+2\hat{j})N$ and $\overrightarrow{F_2}=(3\hat{j}+4\hat{k})N$ are acting on a particle. The angle between $\overrightarrow{F_1}\text{and}\overrightarrow{F_2}$ is

Acceleration - displacement graph for four practices are shown, identify the one which represent SHM for all displacements ?

Five identical rods are joined as shown in figure. Point A and C are maintained at temperature ${120}^{\circ }C$ and ${20}^{\circ }C$ respectively. The temperature of junction B will be