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A steel wire is suspended vertically from a rigid support. When loaded with a weight in air, it extends by $l_a$ and when the weight is immersed completely in water, the extension is reduced to $l_w$. Then the relative density of material of the weight is

Cylinders $\text{B}$ and $\text{C}$ are fixed and cylinder $\text{A}$ is kept above them as shown in figure.





If the system is at rest, find the normal reaction at the contact point of $\text{A}$&$\text{B}$.

$($all cylinders are identical and have mass $m)$

A projectile is fired with an initial speed of $5\text{m/s}$ at an angle of ${45}^{\circ }$with the horizontal, up an inclined plane having angle of inclination ${30}^{\circ }$ from horizontal. What is the range of this projectile?

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

Magnifying power of a simple microscope is (when final image is formed at D = 25 cm from eye)

[MP PET 1996; BVP 2003]

A thin prism of angle $6^{\circ }$ made of glass of refractive index $1.5$ is combined with another thin prism made of glass of refractive index $1.75$ to produce dispersion without deviation. The angle of the second prism is :

Two strings with masses per unit length of $25\text{gm/cm}$ and $9\text{gm/cm}$ are joined together in series. The reflection coefficients for the vibration waves is

A rod of length $10\text{cm}$ made up of conducting and non-conducting material (shaded part is non-conducting). The rod is revolving with constant angular velocity of $10\text{rad/s}$ about point $O$, in a constant magnetic field of $2\text{T}$ perpendicular to the plane of rotation of the rod as shown in the figure. The induced emf between the point $A$ and $B$ is -

Two small balls of masses ${}^{\prime }{m}^{\prime }$ and ${}^{\prime }2m^{\prime }$ are placed in a fixed smooth horizontal circular hollow tube of mean radius ${}^{\prime }{r}^{\prime }$ as shown. The ball of mass ${}^{\prime }{m}^{\prime }$ is moving with speed ${}^{\prime }{u}^{\prime }$ and the ball of mass ${}^{\prime }2m^{\prime }$ is stationary. After their first collision, the time elapsed for next collision is: (coefficient of restitution $e$ = $\frac{1}{2}$)

In a cam-follower , the follower rises by h as the cam rotates by $\delta$ (radians) at constant angular velocity $\omega$ (radians/s). The follower is uniformly accelerating during the first half of the rise perod of the rise period, and it is uniformly decelerating in the later half of the rise period. Assuming that the magnitudes of the acceleration and deceleration are same, the maximum velocity of the follower is

Two smooth blocks of masses $m_1$ and $m_2$ attached with an ideal spring of stiffness $k$ and kept on a horizontal surface. If $m_1$ is projected with a horizontal velocity $v_0$. Find the maximum compression of the spring.

A cricket ball of 0.5 kg is moving with a velocity of 100 m/sec. The wavelength associated with its motion is

A small sphere of radius $r$ and mass $m$ oscillates back and forth on a smooth concave surface of radius $R$ as shown in figure. Find the time period of small oscillations.

A particle of mass $20\text{g}$ is thrown vertically upwards with a speed of $10\text{m/s}$. Find the work done by the gravity during the time of ascent of the particle.

A wave with a frequency of 30 Hz travels along a string at speed of 36 m/s and reflects off a free end. The distance of the first node from the end of the string

When the switch is closed, then the initial current through $1\Omega$ resistor in the given circuit is (Consider the capacitor uncharged initially)

A coil having n turns and resistance R ohm is connected with a galvanometer of resistance 4R ohm. This combination is moved in a region where magnetic flux changes from $W_{1}weberto{W}_2$ weber in t second. The induced current in the circuit is

A 5.0 W laser emits monochromatic light of frequency 8.0 $\times {10}^{14}Hz$. The number of photons emitted per second by the laser is

Two electric bulbs, rated at (40 W, 220 V) and (160 W, 220 V) are connected in series at 110 V. If power drawn by bulb 1 (40 W) is $P_1$ & bulb 2 (160 W) is $P_2$, then

Find potential drop across capacitors $C_2$, $C_4$ and $C_5$ in the given circuit?

In the following arrangement the system is initially at rest. The 5 kg block is now released. Assuming the pulleys and string to be massless and smooth, the acceleration of blocks are

1. 4

A MAN OF MASS 60 KG IS STANDING ON A WEIGHING MACHINE OF MASS 5 KG PLACED ON THE GROUND .ANOTHER SAME WEIGHING MACHINE IS PLACED OVER MANS HEAD A BLOCK OF MASS 60 KG IS PUT ON THIS WEIGHING MACHINE.CALCULATE THE READINGS OF WEIGHING MACHINES 1 AND 2

A rope is being pulled with a force of $100N$ and $80N$ in opposite directions. The net force acting on the rope is