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1. 1.75

A length scale $\left(l\right)$ depends on the permittivity $\left(\epsilon \right)$ of a dielectric material, Boltzmann constant $\left(k_B\right)$, the absolute temperature $\left(T\right)$, the number per unit volume$\left(n\right)$ of certain charged particles and the charge $\left(q\right)$ carried by each of the particles. Which of the following expression(s) for $l$ is(are) dimensionally correct?

In terms of Rydberg's constant $R$, the wavenumber of first line of Balmer series is,

A force $\overrightarrow{F}=3\hat{i}+2\hat{j}-4\hat{k}$ acts at the point $(1,-1,2)$. Find its torque about the point $(2,-1,3).$

The surface tension of a liquid is $70\text{dyne/cm}$. In MKS system its value is

An ideal gas is filled in a cylinder, which is fitted with a movable non-conducting piston as shown in the figure. The gas in the cylinder is heated slowly. The gas expands and pistons moves towards right. If the temperature of the gas is increased slowly from $T_0$ to $2T_0$, find the displacement of the piston. (Given atmospheric pressure = $P_0$ and area of cross-section of the cylinder = $A$).

The average velocity of molecules of a gas of molecular mass $M$ at temperature $T$ is

In deriving Bernoulli’s equation, we equated the work done on the fluid in the tube to its change in the potential and kinetic energy. (a) What is the largest average velocity of blood flow in an artery of diameter $2\times {10}^{–3}$ m if the flow must remain laminar? (b) Do the dissipative forces become more important as the fluid velocity increases? Discuss qualitatively.

A projectile of mass $0.5\text{kg}$ is thrown with a velocity of $30\text{m/s}$ at an angle of ${60}^{\circ }$ with the horizontal. Find the net force acting on the body when in air. (Take $g=9.8m/s^2$)

Four particles each of mass $m$ are placed at the corners of a square of side length $l$. The radius of gyration of the system about an axis perpendicular to the square and passing through its centre is

A block of weight $5N$ is pushed against a vertical wall by a force $12N$. The coefficient of friction between the wall and block is $0.6$. The magnitude of the net contact force will be

A body of mass $1kg$ is moving with a velocity $v=10\hat{i}+5\hat{j}$ m/s. What is the angle made by the momentum vector with $x-$ axis?

For the two fixed infinite line charges, the net electric field is zero at a point $\text{P}$ between them. The distance of the point $\text{P}$ from the left infinite line charge is

In the adjoining figure, the coefficient of friction between wedge (of mass M) and block (of mass m) is $\mu$.

Find the minimum horizontal force F required to keep the block stationary with respect to wedge.

An object is thrown vertically upward with a velocity of $10{\text{ms}}^{-1}$ from the ground. It strikes the ground after____ seconds. (Take $g=10{\text{ms}}^{-2})$

In a compound microscope, the focal length of two lenses are $1.5\text{cm}\text{and}6.25\text{cm}$. An object is placed at $2\text{cm}$ from objective and the final image is formed at $25\text{cm}$ from the eyepiece. The distance between the two lens is (in $\text{cm}$ )

a metal sphere of radius 5 cm is charged such that the potential on its surface is 10 v . What is potential at centre of sphere?

The acceleration of the particle moving in positive $x-$direction with an initial velocity of $10\text{m/s}$ is $3{\text{m/s}}^2$. Its velocity at $t=4sec$ is

A car is moving on a circular path with a constant speed of $10m/s$. What is the magnitude of change in velocity when it moves through ${120}^{\circ }$?

A particle of mass m moving in the x direction with speed 2v is hit by another particle of mass 2m moving in the y direction with speed v. If the collision is perfectly inelastic, the percentage loss in the energy during the collision is close to:

Two long wires AB and CD carry currents i₁
and i₂ in the direction shown in figure.

To see the virtual image of an object formed in the lens, the object and the observer should be:

Kinetic energy of a comet moving in space is given by $k=\frac{\alpha m}{s^2}$ (where m is the mass of comet, and s is the distance travelled by comet. Determine dimensions of $\alpha .$

A car travelling at 60 km/h overtake another car travelling at 42 km/h. Assuming each car to be 5m long, find the time taken during the overtake and the total road distance used for the overtake.

One
end of a string of length l
is
connected to a particle of mass m
and the
other to a small peg on a smooth horizontal table. If the particle
moves in a circle with speed v
the net
force on the particle (directed towards the centre) is:

(i) T,
(ii) ,
(iii) ,
(iv) 0

T
is the
tension in the string. [Choose the correct alternative].

Which one of the following spherical lenses (shown with radius of curvature) doesn't exihibit dispersion?

An uncharged capacitor is connected to a $15\text{V}$ battery through a resistance of $10\Omega$. It is found that in a time of $2\mu \text{s},$ potential difference across the capacitor becomes $5\text{V}$. Find the capacitance of the capacitor. Take $(\ln 1.5=0.4)$

Power of black body radiation versus wavelength for three different temperature is given below. Then select the correct option.

For the circuit given below, evaluate the current (I) passing through $2\Omega$.