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A solid cylinder of mass 'm' and radius 'R' rests on a plank of mass '2m' lying on a smooth horizontal surface. String connecting the cylinder to the plank is passing over a massless pulley mounted on a movable light block B, and the friction between the cylinder and the plank is sufficient to prevent slipping. If the block B is pulled with a constant force 'F', find the acceleration of the cylinder and that of the plank.

If $\overrightarrow{A}=\hat{i}+\hat{j}+\hat{k}$ and $\overrightarrow{B}=2\hat{i}-\hat{j}+3\hat{k}$. Find the angle between $\overrightarrow{A}$ and $\overrightarrow{B}$.

A laser beam has intensity $I$. What is the amplitude of electric field in the beam?

What does permittivity mean in context to electrons?

For the given equation $\sqrt{2}{x}^2-3x+\sqrt{2}=0$, the value of roots are

A small disc is set on rolling with speed $10\text{m/s}$ on the horizontal part of the track from right to left. There is curved part also as shown in the figure. To what height will the disc climb up on the curved path ? Assuming all track is rough and there is no slipping occur anywhere.

Which of the following nuclei shown in the graph is light and stable?

Sixteen identical resistors, each having resistance $R$ are connected as shown in the figure. Find the net resistance between points $X$ and $Y$.

A ray of light of intensity I is incident on a parallel glass-slab at a point A as shown in fig. It undergoes partial reflection and refraction. At each reflection 25% of incident energy is reflected. The rays AB and A'B' undergo interference. The ratio is

[IIT 1990]

Which law governs the phenomenon that a tablecloth is pulled out from under a setting of chinaware without damaging it?

A heated body emits radiation which has maximum intensity near the frequency $v_0$. The emissivity of the material is $0.5$. If the absolute temperature of the body is doubled, the maximum intensity of radiation will be near the frequency

I, II and III are three isotherms respectively at $T_1$, $T_2$ and $T_3$ temperatures. The order of temperature will be

A SONAR system fixed in a submarine operates at a frequency 40.0
kHz. An enemy submarine moves towards the SONAR with a speed of 360
km h^–1. What is the frequency of sound reflected by
the submarine? Take the speed of sound in water to be 1450 m s^–1.

Two magnetic dipoles $X$ and $Y$ are placed at a separation $d$, with their axes perpendicular to each other. The dipole moment of $Y$ is twice that of $X$. A particle of charge $q$ is passing through their midpoint $P$, at angle $\theta =45°$ with the horizontal line, as shown in figure. What would be the magnitude of force on the particle at that instant ? ($d$ is much larger than the dimensions of the dipole)

Blocks of masses $m,2m,4m$ and $8m$ are arranged in a line on a frictionless floor. Another block of mass $m,$ moving with speed $v$ along the same line (as shown) collides with mass $m$ in a perfectly inelastic manner. All the subsequent collisions are also perfectly inelastic. By the time the last block of mass $8m$ starts moving, the total energy loss is $p\%$ of the original energy. The value of $p$ is close to-

If the system in the figure is released from rest in the configuration shown, find the velocity of the block $Q$ after it has fallen through a distance $10\text{meters}$. Given $P=Q=10\text{kg}$.

If a direct current of value $a$ ampere is superimposed on an alternating current $I=b\sin \omega t$ flowing through a wire, what is the effective value of the resulting current in the circuit?

A train moves at a constant speed of 60.0 km/h towards east for 30 min, then in a direction ${30}^{\circ }$ east of due north for 20.0 min, and then west for 45 min. What are the (a) magnitude and (b) angle of its average velocity during this trip?

A fun drive in an amusement park runs between two spots that are $2.0\text{km}$ apart. For safety reasons the acceleration of the drive is limited to $\pm 4.0{\text{m/s}}^2$, and the jerk, or rate of change of acceleration, is limited to $\pm 1.0{\text{m/s}}^2$. The drive has a maximum speed of $144\text{km/h}$. Find the shortest time taken by the driver to travel between the spots?

A radio can tune over
the frequency range of a portion of MW broadcast band: (800 kHz to
1200 kHz). If its LC circuit has an effective inductance of
200 μH, what must be the
range of its variable capacitor?

[Hint: For
tuning, the natural frequency i.e., the frequency of free
oscillations of the LC circuit should be equal to the
frequency of the radiowave.]

Water leaks out from an open tank through a hole of area 2 $m{m}^2$ in the bottom. Suppose water is filled up to a height of 80 cm and the area of cross section of the tank is 0.4 $m^2$. The pressure at the open surface and at the hole are equal to the atmospheric pressure. Neglect the small velocity of the water near the open surface in the tank. (a) Find the initial speed of water coming out of the hole. (b) Find the speed of water coming out when half of water has leaked out. (c) Find the volume of water leaked out during a time interval dt after the height remained is h. Thus find the decrease in height dh in terms of h and dt. (d) From the result of part (c) find the time required for half of the water to leak out.

1. 209.041

The equation ( P + a/V^2)(V-b) = constant

Find the units of a.

$ta{n}^{-1}\sqrt{3}-se{c}^{-1}(-2)$ is equal to
a) $\pi$
b) $-\frac{\pi }{3}$
c) $\frac{\pi }{3}$
d) $\frac{2\pi }{3}$

The specific heat capacity of a metal is $0.01{\text{cal/g}}^{\circ }\text{C}$. If heat capacity of $m\text{kg}$ of metal is $0.42\text{J}{/}^{\circ }\text{C}$. Find the value of $m$.

Explain
why:

(a) a
body with large reflectivity is a poor emitter

(b) a
brass tumbler feels much colder than a wooden tray on a chilly day

(c) an optical pyrometer (for measuring high
temperatures) calibrated for an ideal black body radiation gives too
low a value for the temperature of a red hot iron piece in the open,
but gives a correct value for the temperature when the same piece is
in the furnace

(d) the
earth without its atmosphere would be inhospitably cold

(e) heating systems based on circulation of steam
are more efficient in warming a building than those based on
circulation of hot water

Light of wavelength $500nm$ is incident on a metal with a work function of $2.28eV$. The de borglie wavelength of the emitted electron is

What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an altitude of 2R?

A ball is released from the top of a tower of height $h$. It takes time $T$ to reach the ground. What is the position of the ball (from ground) after time $\frac{T}{3}$?

A block of mass $10kg$ is connected to another block of mass $20kg$ by a massless spring of spring constant $k$. The blocks are kept on a smooth horizontal plane. Initially, the blocks are at rest and the spring is unstretched. Then a constant force $200N$ starts acting on the block of mass $20kg$ to pull it. Find the force on the block of mass $10kg$ in $N$, if the acceleration of both blocks are same.

A count rate meter shows a count of 240 per minute from a given radioactive source. One hour later the meter shows a count rate of 3.0 per minute. The half life of the source is

Find the acceleration of the block A and B in the three situations shown in figure.

A satellite is revolving around earth in a circular orbit of radius $2R$, where $R$ is the earth's radius. A particle is projected from this satellite radially outward relative to satellite with speed $u$. Find the minimum value of $u$ so that particle escapes the gravitational force of earth. $M$ is the mass of earth. (Mass of earth >>> Mass of satellite >>> Mass of particle)

A body undergoes a free fall. Taking downward direction as +ve $Y$ direction and $Y_o$ is the initial position, $Y$ coordinate at any time $t$ is given by

When a belt moves horizontally at a constant speed of $1.5{\text{ms}}^{-1},$ gravels are falling on it at rate of $5$ ${\text{kg s}}^{-1}.$ Then, the extra power required to drive the belt is