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Find the acceleration ( in ${\text{m/s}}^2$) of $2\text{kg}$ block in the figures $\left(A\right)$ and $\left(B\right)$ shown at the instant when $1\text{kg}$ block falls from $2\text{kg}$ block (at $t=0$). (Systems are in equilibrium at $t=0$)

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

By what minimum angle the mirror must be rotated anticlockwise such that the reflected ray will become vertical?

A $2\mu \text{F}$ capacitor is charged to a potential difference of $10\text{V}$. Another $4\mu \text{F}$ capacitor is charged to a potential difference of $20\text{V}$. The two capacitors are then connected in a single loop, with the positive plate of one connected with negative plate of another. What is the amount of heat dissipated in the circuit ?

An object is places at a distance 40 cm from a thin converging lens of focal length; 10cm. Calculate the image distance.

A force $10\text{N}$ acts tangentially at the highest point of a solid sphere of mass $10\text{kg}$ kept on a rough horizontal plane. If the sphere rolls without slipping, find the acceleration of the centre of the sphere (in $\text{m}/{\text{s}}^2$).

A point charge $Q(=3\times {10}^{-12}C)$ rotates uniformly in a vertical circle of radius R = 1 mm. The axis of the circle is aligned along the magnetic axis of the earth. At what value of the angular speed $\omega$, the effective magnetic field at the center of the circle will be reduced to zero? (Horizontal component of Earth’s magnetic field is 30 micro Tesla)

Two rods $P$ and $Q$ have equal lengths. Their thermal conductivities are $K_1$ and $K_2$ and cross-sectional areas are $A_1$ and $A_2$. When the temperature at ends of each rod are $T_1$ and $T_2$ respectively, the rate of flow of heat through $P$ and $Q$ will be equal, if

A beaker is filled with water to its brim and a ball of mass 100 kg into it. The amount of water displaced is 10 kg. Find the buoyant force experienced by the ball.

Two stones are thrown vertically upwards simultaneously from the same point on the ground with velocities $u_1=40m/s\text{and}{u}_2=30m/s$. Which of the following curve(s) represent(s) correct variation with time t ? (Assume that stone does not bounce back after collision with ground) $(y_1–y_2)=$ relative separation between stones (v1 – v2) = relative velocity of two stones $(a_1–a_2)=$ relative acceleration of two stones

Diameter of the moon is $3.5\times {10}^{3}km$ and its distance from the earth is $3.8\times {10}^{5}km$. It is seen by a telescope whose objective and eyepiece have focal lengths $4m$ and $10cm$ respectively. The angular diameter of the image of the moon is (assume final image is at infinity)

Evaluate: ${\int }_2^5\text{(ln x)dx}$

A machine gun fires 60 bullets per minute with a velocity of 700m/s . If the mass of each bullet is 50g , calculate the power of gun .

The linear momentum of a system of particles is the sum of linear momenta of the individual particles . Can we state a principle of conservation of linear momentum as "linear momentum of a system remains constant if no external force acts on it"???

Two identical balls marked 2 and 3, in contact with each other and at rest on a horizontal frictionless table, are hit head-on by another identical ball marked 1 moving initially with a speed 'v' as shown in the figure. If the collision is elastic, what is observed?

A small
telescope has an objective lens of focal length 144 cm and an
eyepiece of focal length 6.0 cm. What is the magnifying power of the
telescope? What is the separation between the objective and the
eyepiece?

Following figure shows on adiabatic cylindrical container of volume V_o divided by an adiabatic smooth piston (area of cross-section = A) in two equal parts. An ideal gas is at pressure P₁ and temperature T₁ in left part and gas at pressure P₂ and temperature T₂ in right part. The piston is slowly displaced and released at a position where it can stay in equilibrium. The final pressure of the two parts will be (Suppose x = displacement of the piston)

A ray of light falls on one face of an equilateral glass prism at ${40}^{\circ }$ and emerges from the other face at the same angle. The deviation suffered by the ray is

For small volumes of gas, according to kinetic theory of gases all parts of the gas are at the same temperature. But for huge volumes of gas like atmosphere, the assumption of a uniform temperature throughout the gas is not valid. Apart from the surface of earth, variation in temperature also occurs at different heights in atmosphere. The decrease in temperature with height called the "Atmospheric lapse rate" is similar at various locations it is found that average global lapse rate is $-{6.7}^{\circ }\text{C/km}$. The linear decrease in temp with height occurs in the lower part of atmosphere called troposphere. Absorption of sunlight at earth's surface warms the troposphere from below. So convection currents are continually produced in the air, and causes its mixing.

As a parcel of air rises, its pressure drops and it expands. The parcel does work on its surroundings thus its internal energy and temperature drops.

Assume that the vartical mixing of air is so rapid as to be adiabatic and the quantity $T{P}^{\frac{(1-\gamma )}{\gamma }}$ has a uniform value throughout the layer of troposphere.

(Given: $M$ is molecular weight of air, $R$ being the universal gas constant, $P$ and $T$ are pressure and temperature respectively at a point under consideration at a height $y$)

If the mechanical equilibrium of atmosphere requires that the pressure decreases with altitude according to $\frac{dp}{dy}=-\rho g$ consider $g$ to be constant, the lapse rate is given by:

The energy of a photon emitted in a Bohr atom due to electronic transitions from one orbit to the other is:

A light wave of wavelength ${\lambda }_0$ propogates from point $A$ to point $B$. We introduce in its path a glass plate of refractive index $n$ and thickness $l$. The introduction of the plate alters the phase of the plate at $B$ by an angle $\varphi$. If $\lambda$ is the wavelength of light on emerging from the plate , then

Three charges q, q and - 2q are fixed on the vertices of an equilateral triangular plate of edge length a. This plate is in equilibrium between two very large plates having surface charge density ${\sigma }_1$ and ${\sigma }_2$ respectively. Find time period of small angular oscillation about an axis passing through its centroid and perpendicular to plane. Moment of inertia of the system about this axis is I.

Helium gas goes through a cycle $\text{ABCDA}$ (consisting of two isochoric and two isobaric lines) as shown in figure. Efficiency of this cycle is nearly:

[Assume the gas to be an ideal gas]

In the given circuit the readings of voltmeter $V_1$ and $V_2$ are 300 volts each. The readings of the voltmeter $V_3$, and ammeter A are respectively