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Flow rate of a fluid ( $\rho =1000kg/m^3$) in a small diameter tube is $800m{m}^3/s$. The length and diameter of the tube are 2 m and 0.5 mm, respectively. The pressure drop in 2 m length of is equal to 2 MPa. The viscosity of the fluid is:

An AC circuit contains a resistor of $10\Omega$ and an inductor of $2.0\text{H}$, joined in series. If an AC voltage source of $120\text{V},60\text{Hz}$ is applied across this circuit, the peak AC will be -

In the arrangement shown in the figure, mass of the block $B$ and $A$ are $2m$, $8m$ respectively. Surface between $B$ and the floor is smooth. The block $B$ is connected to block $C$ by means of a pulley. If the whole system is released from rest, then find the minimum value of mass of block $C$ so that the block $A$ remains stationary with respect to $B$. Given coefficient of static friction between $A$ and $B$ is $\mu$ and pulley is ideal.

Charges $-q$ and $+q$ located at $\text{A}$ and $\text{B}$ respectively and $\text{OP}$ is perpendicular to line $\text{AB}$. A charge $Q$ is placed at $\text{P}$, where $\text{OP}=y$ $(y>>2a)$. The charge $Q$ experiences an electrostatics force $F$. If $Q$ is now moved along the equatorial line to $P^{\prime }$ such that $O{P}^{\prime }=\frac{y}{3}$, the force experienced by charge $Q$ will be close to

$(\text{Assume}\frac{y}{2}>>2a)$

A convex lens has a focal length of 10cm. What is the power of the lens?

A stone falls from a balloon that is descending at a uniform rate of 12 m/s. The magnitude of the displacement of the stone from the point of release after 10 sec is

A particle moves with constant speed v along a circular path of radius r and completes the circle in time T. The acceleration of the particle is

A car moves on a circular road. It describes equal angles about the centre in equal intervals of time. Which of the following statement about the velocity of the car is true

A flat square sheet of charge ( side 50 cm) carries a uniform surface charge density. An electron 0.5 cm from a point near the center of the sheet experiences a force of 1.8 * 10^-12 N directed away from the sheet. Determine the total charge on the sheet.

Two particles, one with constant velocity of $50{\text{ms}}^{-1}$ and the other with uniform acceleration $10{\text{ms}}^{-2}$, start moving simultaneously from the same place in the same direction. When will the accelerated particle be $125\text{m}$ ahead of the other particle?

Two cars are $15m$ apart as shown in the figure at time $t=0$. Find the closest distance between the cars. (Velocity of cars are as shown in the figure)

Find $\overrightarrow{A}\times \overrightarrow{B}$, if $\overrightarrow{A}=\hat{i}+2\hat{j}-4\hat{k}$ and $\overrightarrow{B}=2\hat{i}-\hat{j}+2\hat{k}$.

An ideal inductor is connected in series with a resistor and an ideal battery. The battery supplies energy at a rate P(t), the resistor dissipates energy at a rate $P_R\left(t\right)$, and the inductor stores energy at a rate $P_L\left(t\right)$. What can be concluded about the relationship between $P_R\left(t\right)$ and $P_L\left(t\right)$?

Two charged spheres separated at a distance d exert a force F on each other. If they are immersed in a liquid of dielectric constant 2, then the force (if all conditions are same) on each sphere is

A proton and an $\alpha -$particle are accelerated through a potential difference of $200\text{V}$. The ratio of the de-Broglie wavelengths associated with the proton to that with an $\alpha -$particle is,

A particle is projected from the ground with an initial velocity of $20m/s$ at an angle of ${30}^{\circ }$ with horizontal. The magnitude of change in velocity in a time interval from $t=0$ to $t=0.5s$ is

$(g=10m/s^2)$

The time taken by a particle executing simple harmonic motion to move from the mean position to $(1/4{)}^{th}$ of the maximum displacement is $1\text{s}$. Calculate the angular frequency of oscillation.

$\left[{\sin }^{-1}\right(1/4)=0.252]$

A gas at certain volume and temperature has a pressure equal to $75\text{cm}$ of mercury column. If the mass of the gas is doubled, at the same volume and temperature, its new pressure is

In a charging circuit having resistance $R=0.5\text{M}\Omega$ and capacitance, $C=2\mu \text{F}$, after what time will the energy stored in the capacitor reach to $75\%$ of its maximum value?

A stone is projected from the ground and hits a smooth vertical wall after $1\text{s}$ and again fall back on the ground as shown in the figure. The time taken by the stone to reach the ground after the collision is $3\text{s}$. The maximum height reached by the same stone if the vertical wall is not present will be

(Take $g=10{\text{m/s}}^2$)

Refractive index of violet, yellow and red color of light for a material of lens are $1.66,1.64$ and $1.62$ respectively. If mean focal length of lens is $10\text{cm}$. Then chromatic aberration between the color of viole and red will be

A reversible heat pump is driven by the work output of a reversible heat engine, as shown in the figure below. If we assume ideal devices, then what will be the ratio of the total power ${\dot{Q}}_{L1}+{\dot{Q}}_{H2}$ heats the house to the power from the hot energy source ${\dot{Q}}_{H1}$ in terms of the temperature

An old man goes for morning walk on a semi-circular track of radius $30\text{m}$, if he starts from one end of the track and reaches to other end, the distance covered by the man will be

An object is displaced from point $A(2,3,4)m$ to a point $B(1,2,3)m$ under the influence of a force $\overrightarrow{F}=2\hat{i}+3y^2\hat{j}+5\hat{k}.$ The workdone by this force is

A thin wire of $99\text{cm}$ is fixed at both ends as shown in figure. The wire is kept under a tension and is divided into three segments of lengths $l_1,l_2$, and $l_3$ as shown in figure. If the wires are made to vibrate, with their fundamental frequencies respectively in the ratio $1:2:3$, then the lengths $l_1,l_2,l_3$ of the segments respectively are (in $\text{cm}$):

The temperature of a hypothetical gas increases to $\sqrt{2}$ times when compressed adiabatically to half the volume. Its equation can be written as

A 1500-kg car moving o a flat, horizontal road negotiates a curve as show in figure. If the radius of the curve is 20.0 m and the coefficient of static friction between the tires and dry pavement is 0.50, find the maximum speed the car can have and still make the turn successfully.

Assume that the batteries in the figure have negligible internal resistance. The current in the circuit is-

Unpolarized light of intensity I passes through an ideal polarizer A. Another identical polarizer $B$ is placed behind $A$. The intensity of light beyond $B$ is found to be $\frac{I}{2}.$ Now another identical polarizer $C$ is placed between $A$ and $B$. The intensity beyond $B$ is now found to be $\frac{I}{8}.$ The angle between polarizer $A$ and $C$ is :

An elastic force sensor has an effeictive seismic mass of $0.1kg$, a spring stiffeness of $10N/m$ and a damping constant of $14N-s/m.$ Transfer function of the given force sensor relating displacment and force is given by

A gas mixture consists of 2 moles of oxygen and 4 moles of argon at temperature $T$. Neglecting all vibrational modes, the total internal energy of the system is

A simple pendulum of bob mass m is oscillating with an angular amplitude ${\alpha }_m$ (in radian). The maximum tension in the string is