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The time constant of an inductance coil is 4 ms. On connecting a resistor of $60\Omega$ in series with it, the time constant is reduced to 1 ms. The inductance and resistance of the coil are respectively

A particle starts executing S.H.M. of amplitude a and total energy E. At the instant its kinetic energy is $\frac{3E}{4}$ , its displacement y is given by

On a cylindrical rod two coils are wound one over the other. If the inductance of each coil is 0.1 H the mutual inductance of the pair of coils is

In a series $LCR$ circuit $L=10mH$, $C=1$ $\mu F$ and $R=3$$\Omega$. It is connected to an AC voltage source. The inductive reactance of the circuit at a frequency $25$% less than resonant frequency is

A particle of mass $1kg$ is projected with a velocity of $20m/s$ at an angle of ${30}^{\circ }$ with the horizontal. Find the change in the momentum $(kg-m/s)$ of the particle between the points of projection and the highest point. Take $g=10m/s^2$

Three capacitors are connected as shown in figure. Then the charge on capacitor plate $C_1$ is:

A sound absorber attenuates the sound level by $20dB$. The intensity decreases by a factor of

Determine the relationship that governs the velocities of four cylinders if $v_A$, $v_B$, $v_C$ and $v_D$ represents velocities of block A, B, C and D. Consider downward velocity as positive and strings inextensible.

A bat emitting an ultrasonic wave. of frequency $4.5\times {10}^4$ Hz flies at a speed of 6 m/s between two parallel walls. Find the two frequencies heard by the bat and the beat frequency between the two. The speed sound is 330 m/s.

A curved road of $50\text{m}$ radius is banked at correct angle for a given maximum speed $vm/s$. If the radius of curvature of the road is changed to $200\text{m}$ keeping the same banking angle, the maximum safe speed on the road is

Find the minimum force P required to move block of weight W up the incline plane

A ring of mass $2\pi \text{kg}$ and radius $0.25\text{m}$ is making $300\text{rpm}$ about an axis perpendicular to its plane. The tension (in newtons) developed in the ring is, approximately

Point masses of 1,2,3 and 10 kg are lying at the point (0 0) (2 0) (0 3 )(- 2 - 2) respectively. In x-y plane, the moment of inertia of the system about y axis will be in Kg metre2

A $100\text{kg}$ block is dropped from the top of a building $80\text{m}$ tall. Assume $g=10{\text{ms}}^{-2}$. Find the work done by the force of gravity as it falls vertically to hit the ground.

A table clock has its minute hand $4cm$ long. Find the average velocity of the tip of the minute hand (a) between 6 AM to 6:30 AM and (b) between 6 AM to 6:30 PM

Intensity level 2 cm from a source of sound is 80 dB. If there is no loss of acoustic power in air and intensity of threshold hearing is ${10}^{-12}$ $W{m}^{-2}$ then, what is the intensity level at a distance of 40 cm from source?

The number of photons emitted by a 5mW laser source operating at 632.8 nm is __$\times {10}^{16}$

Two discs, each of mass M and radius R is placed parallel to each other at a distance d about a common axis as shown in the figure. The moment of inertia of the system about $Y{Y}^{\prime }$ axis.

The density of the material of a cube is measured by measuring its mass and length of its side. If the maximum error in the measurement of mass and the length are $3\%$ and $2\%$ respectively, the maximum error in the measurement of density is

At time t = 0, apple 1 is dropped from a bridge onto a roadway beneath the bridge; somewhat later, apple 2 is thrown down from the same height. Figure below gives the vertical position, y of the apples versus t, time of the falling, until both apples have hit the roadway. The scaling is set by $t_s$= 2.0 s. With approximately what speed was apple 2 thrown down?

Two charges $+3.2\times {10}^{-19}C$ and $-3.2\times {10}^{-19}C$ placed at $2.4\stackrel{o}{A}$ apart to form an eletric dipole. It is placed in a uniform electric field of intensity $4\times {10}^5\text{volt/m}$. The electric dipole moment is

The average velocity of a body moving with uniform acceleration after traveling a distance of 3.06m is 0.34m/s if the change in velocity of the body is 0.18m/s during this time it's uniform acceleration is?

A balloon is released from the ground $(h=0\text{m})$ from rest and starts accelerating with acceleration $5{\text{m/s}}^2$ vertically upwards. An object is dropped from the balloon, when it is at height $10\text{m}$ from the ground. If the balloon is released at $t=0\text{sec}$, then find the time when the object reaches the ground. Take $g=10{\text{m/s}}^2$.

With the assumption of no slipping, determine the mass m of the block which must be placed on the top of a 6 kg cart in order that the system period is 0.75 s.

A particle in SHM is described by the displacement

equation x(t) = A cos ( $\omega t+\theta )$ . If the initial (t = 0)

position of the particle is 1 cm and its initial

velocity is $\pi$ cm/s, what is its amplitude?

The angular frequency of the particle is $\pi s^{-1}$

A player kicks a football at an angle of ${45}^{\circ }$ with a velocity of $30m{s}^{-1}$. A second player $120m$ away along the direction of kick starts running to receive the ball at that instant. Find the speed with which second player should run to reach the ball before it hits the ground $(g=10m{s}^{-2})$

When a system is taken from state $‘a^{\prime }$ to state $‘b^{\prime }$ along the path $‘ac{b}^{\prime }$, it is found that a quantity of heat $Q=200\text{J}$ is absorbed by the system and a work $W=80\text{J}$ is done by it. Along the path $‘ad{b}^{\prime },Q=144\text{J}$. The work done along the path $‘ad{b}^{\prime }$ is

If force (F), pressure (P) and speed (v) are fundamental quantities, then dimensional formula of time is :

Find the net force acting on pulley $2$ assuming all strings and pulleys to be of negligible mass and all surfaces to be frictionless. $g=10{\text{m/s}}^2$.

If velocity of a particle is $v\left(t\right)=2t-4\text{m/s}$, the average speed and magnitude of average velocity of the particle in $10\text{sec}$ respectively are

Consider two waves passing through the same string. Principle of superposition for displacement says that the net displacement of a particle on the string is sum of the displacements produced by the two waves individually. Suppose we state similar principles for the net velocity of the particle and the net kinetic energy of the particle. Such a principle will be valid for

For an ideal gas, the slope of $V-T$ graph during an adiabatic process is $\frac{dV}{dT}=-m$ at a point where volume and temperature are $V_0$ and $T_0$. Find the value of $C_P$ of the gas. It is given that $m$ is a positive number.

A thin square plate of side $3\text{m}$ has mass $5\text{kg}$. Find the moment of inertia about axis $AB$ as shown in figure.

A quantity of air is taken from state a to state b along a path that is a straight line in the P-V diagram. In the previous question If Va = 0.0700 $m^3$, Vb = 0.1100 $m^3$, Pa = 1.00 $\times$ ${10}^5$ Pa, and Pb = 1.40 $\times$${10}^5$ Pa, what is the work W done by the gas in this process? Assume that the gas may be treated as ideal.

A $40\text{kg}$ girl is swinging on a swing from rest. Then, the power delivered when moving with a velocity of $2\text{m/s}$ upwards in a direction making an angle ${60}^{\circ }$ with the vertical is

If $2$ moles of an ideal monoatomic gas at temperature $T_0$ is mixed with $4$ moles of another ideal monoatomic gas at temperature $2T_0$, then the temperature of the mixture is

A rope 1 cm in diameter breaks if the tension in it exceeds 500N. The maximum tension that may be given to a similar rope of diameter 2 cm is?

A thin equiconvex lens is made of glass of R.I 1.5 and its focal length is 0.2 If it acts a concave lens of 0.5 m focal length when dipped in a liquid, the R.I of liquid is

Two blocks of equal mass m are tied to each other through a light string. One of the blocks is pulled along the line joining them with a constant force F. Find the tension in the string joining the blocks.