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The molar heat capacity of a gas at constant volume is $5{\text{cal mol}}^{-1}{\text{K}}^{-1}$. Find the value of $\gamma$ for the gas if the gas constant, $R=2{\text{cal mol}}^{-1}{\text{K}}^{-1}$.

The loudness of sound depends upon _______.

A point $P$ moves in clockwise direction on a circular path as shown in figure. The movement of $P$ is such that it sweeps a distance $s=2t^3+3t^2+6$, where $s$ is in metres and $t$ is in seconds. The radius of the path is $36\text{m}$. The acceleration of ${}^{\prime }{P}^{\prime }$ when $t=1\text{s}$ is

The torque experienced by a given current carrying loop in a uniform magnetic field $\overrightarrow{B}=B_0(\hat{i}-\hat{j})$ would have magnitude

A bob is hanging over a pulley inside a car through a string. The second end of the string is in the hands of a person standing in the car. The car is moving with constant acceleration $a$ directed horizontally as shown. The other end of the string is pulled with constant acceleration $a$ vertically down. Find the tension in the string.

In an experiment of find the focal length of a concave mirror a graph is drawn between the magnitudes of u and v. The graph looks like

[AIIMS 2003]

Two spheres carrying charges $+6\mu Cand+9\mu C$, separated by a distance d, experiences a force of repulsion F. When a charge of $-3\mu C$ is given to both the sphere and kept at the same distance as before, the new force of repulsion is

A particle of mass m and charge q is released from rest in a uniform electric field E. The kinetic energy attained by the particle after moving a distance x along the electric field is

At $t=0$, a particle starts from $(-2,0)$ and moves towards positive $x-$axis with speed of $v=6t^2+4t\text{m/s}$. The final position of the particle and the distance travelled by the particle respectively, as a function of time are

A mass M is attached to a light inextensible string as shown in the figure. Tension in horizontal part of string is

A stone is dropped into a well in which the level of water is $h$ below the top of the well. If $v$ is velocity of sound, the time $T$ after which the splash is heard is given by

The de-Broglie wavelength of the electron in the ground state of the hydrogen atom is,

(radius of the first orbit of hydrogen atom $=0.53\mathring{\text{A}}$)

A block is shot with an initial velocity of $5\text{m/s}$ on a rough horizontal plane. Find the distance covered by the block till it comes to rest. Given the coefficient of friction between the surfaces of contact is $0.2\text{and}g=10m/s^2$.

A
man stands on a rotating platform, with his arms stretched
horizontally holding a 5 kg weight in each hand. The angular speed of
the platform is 30 revolutions per minute. The man then brings his
arms close to his body with the distance of each weight from the axis
changing from 90cm to 20cm. The moment of inertia of the man together
with the platform may be taken to be constant and equal to 7.6 kg m².

(a) What
is his new angular speed? (Neglect friction.)

(b) Is
kinetic energy conserved in the process? If not, from where does the
change come about?

Find the size of the image formed in the situation shown in figure.

Two wires of the young's modulii $Y$ and $2Y$ having lengths $2L,L$ and radii $2R,R$ respectively, are joined end to end as shown in the image. The elastic potential energy stored in the system in equilibrium, is





[Assume the wires are massless and $w$ is the weight hung at the bottom]

Two strings are tied $2\text{m}$ apart on a rod and on the other end a mass $200\text{g}$ is tied as shown in figure. Each string is $1.25\text{m}$ long. FInd the tensions $T_1$ and $T_2$ if the rod is rotated with $60\text{rpm}$. Consider ${\pi }^2=10$

Two particles and emitted by a radioactive source at made tracks in a cold chamber as illustrated in the figure. A magnetic field acted downward into the paper. Careful measurements showed that both tracks were circular, the radius of Y track being half that of the Z track. Which one of the following statements is certainly true?

[MNR 1980; Pb. CET 1990; DCE 2001]

A capacitor is made of a flat plate of area A and a sector plate having a stair-like structure as shown in figure (31-E9). The width of each stair is a and the height b. Find the capacitance of the assembly.

In Young's double slit experiment, if monochromatic light is replaced by white light

[AIIMS 2001; Kerala PET 2000; KCET 2004]

A flag is hoisted on the steamer boat.On the basis of the data given below find out the direction of flutter of

the flag

${\overrightarrow{v}}_{steamer/water}=10\sqrt{3}m{s}^{-1}$ towards North

${\overrightarrow{v}}_{water}=5m{s}^{-1}$ towards East

${\overrightarrow{v}}_{wind}=5m{s}^{-1}$ towards East

(Assume the wind does not affect the steamer)

A particle has initial velocity $(2\hat{i}+3\hat{j})$ and acceleration $(0.3\hat{i}+0.2\hat{j})$. The magnitude of velocity after $10\text{s}$ will be

A horizontal platform is executing simple harmonic motion in the vertical direction with frequency $f$. A block of mass $m$ is placed on the platform. What is the maximum amplitude of oscillation so that the block is not detached from it ?

A convex lens is held in water. What would be the change in the focal length?

Three capacitors $C_1,C_2$ and $C_3$ of capacitance $4\mu \text{F}$, $3\mu \text{F}$ and $6\mu \text{F}$ are charged upto a potential difference of $5\text{V},6\text{V}$ and $4\text{V}$ respectively. If terminal $\text{a}$ is connected with $\text{f}$, terminal $\text{e}$ is connected with $\text{d}$ and $\text{b}$ is conncted with $\text{c}$, then find the amount of heat produced in the circuit?

A cylindrical bar of 20mm diameter and 1 m length is subjected to a tensile test. Its longitudinal strain is 4 times that of its lateral strain. If the modulus of elasticity is 2 $\times {10}^5$ N/mm${}^2$, then its modulus of rigidity will be

The probability of electrons to be found in the conduction band of an intrinsic semiconductor at a finite temperature

A capacitor of capacitance $C_1=1.0\mu \text{F}$ withstand a maximum voltage $E_1=6.0\text{kV}$ while a capacitor of capacitance $C_2=2.0\mu \text{F}$ can withstand the maximum voltage $E_2=4.0\text{kV}$. For what voltage will the system of these two capacitors with stand , if they both are connected in series ?

The total energy of hydrogen atom when electron is in the first excited state is about $-3.4eV$. The kinetic energy and potential energy of the electron in this state respectively are

One mole of an ideal gas is contained under a weightless piston of a vertical cylinder at a temperature ${27}^{\circ }\text{C}$. The space over the piston opens into the atmosphere. What work has to be performed in order to increase isothermally, the gas volume under the piston to twice its initial value, by slowly raising the piston. (Neglect friction)