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The resistance in two arms of meterbridge are $R=5\Omega$ and $S=1\Omega$ respectively. If error in measurement of null point is $1\text{cm}$, find the error in measurement of resistance.

A parallel plate capacitor made of circular plates each of radius $R=6\text{cm}$ has a capacitance $C=100\text{pF}$. The capacitor is connected to a $230\text{V},AC$ supply with an angular frequency of $300\text{rad/s}$. Determine the amplitude of the magnetic field at point $9\text{cm}$ from the axis between the plates.

The threshold frequency for a certain photosensitive metal is ${\nu }_0$. When it is illuminated by light of frequency $\nu =2{\nu }_0$, the stopping potential for photoelectric current is$V_0$. What will be the stopping potential when the same metal is illuminated by light of frequency $\nu =3{\nu }_0$?

A solid sphere of radius $4\text{cm}$ and a hollow sphere of same material and having outer radius $4\text{cm}$ and inner radius $2\text{cm}$ are heated to the same temperature and allowed to cool in the same room. The ratio of the rate of fall of temperatures is

According to Bohr's model of H-atom, the radius of a stationary orbit is characterized by the principle Quantum number '$n$' is proportional to

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A stone is fastened to one end of a string and is whirled in a vertical circle of radius $10\text{m}$. Find the minimum speed the stone can have at the highest point on the circle.

[Take$g=10{\text{m/s}}^2$]

At $t=0$, a particle starts from $(4,0)$ and moves towards positive $x-$axis with speed of $v=8t+3\text{m/s}$. The final position of the particle as a function of time is

The electrons are emitted in the photoelectric effect from a metal surface

The velocity time graph of a lift moving upwards has been shown below. Let $T_1,T_2$ and $T_3$ be the tensions in the elevator cable during the three time intervals $\Delta t_1,\Delta t_2$ and $\Delta t_3$, then $T_1:T_2:T_3$

A particle moves from a point (1, 2) to a point B (4,3) in x-y plane in 5 seconds. Find the displacement of the particle during this period.

A rod of length $l$ rotates with a uniform angular velocity $\omega$ about its perpendicular bisector. A uniform magnetic field $B$ exists parallel to the axis of rotation. The potential difference between the two ends of the rod is

Two identical conducting spheres, one having an initial charge +Q and the other initially uncharged, are brought into contact.

1. What is the new charge on each sphere?

2. While the spheres are in contact, a positively charged rod is moved close to one sphere, causing a redistribution of charges on the two spheres, so the charge on the sphere closest to the rod has a charge - Q. What is the charge in the other sphere?

A resistor develops $500\text{J}$ of thermal energy in $20\text{s}$ when a current of $1.5\text{A}$ is passed through it. If the current is increased from $1.5\text{A}$ to $3\text{A}$, what will be the energy developed in $20\text{s}$.

The given figure shows the shape of part of a long string in which transverse waves are produced by attaching one end of the string to tuning fork of frequency 250 Hz. What is the velocity of the waves?

A cylindrical tube, open at both ends, has fundamental frequency $n$. If one of the ends is closed, the fundamental frequency will become

A road is banked such that a vehicle can go in the middle of it with a constant velocity of 40 m/s. What will happen if the velocity is decreased and why?

Imagine friction is not present

The maximum angular magnification produced by an astronomical telescope is $30$. If the focal length of the eyepiece is $12.5\text{cm}$, then find the minimum angular magnification produced by it.

Calculate the stress developed inside a tooth cavity filled with copper when hot tea at temperature of ${57}^{\circ }\text{C}$ is drunk. You can take body (tooth) temperature to be ${37}^{\circ }\text{C}$ and ${\alpha }_{Cu}=1.7\times {10}^{-5}{/}^{\circ }\text{C}$, bulk modulus for copper $K_{Cu}=140\times {10}^9{\text{N/m}}^2$

A thermodynamic cycle $xyz$ is shown on a $V-T$ diagram.





The $P-V$ digram that best describe this cycle is : (diagrams are schematic and not to scale)

A point $\rho$ lies on the axis of a ring of mass M and radius $\alpha$, at a distance $\alpha$, from its centre C, A small particle starts from $\rho$ and reaches C under gravitational attraction only.Its speed at C will be

Assuming human pupil to have a radius of $0.25cm$ and a comfortable viewing distance of $25cm$, the minimum separation between two objects that the human eye can resolve at $500nm$ wavelength is

A thin spherical shell of mass M and radius R has a small hole. A particle of mass m is released at the mouth of the hole. Then

A wheel rotation at a speed of 600 rpm (revolutions per minute) about its axis is brought to rest by applying a constant torque for 10 seconds. Find the angular deceleration and the angular velocity 5 seconds after the application of the torque.

Two transparent media $1$ and $2$ are separated by a plane boundary. The speed of light in medium $1$ is $2.0\times {10}^8{\text{ms}}^{-1}$ and in medium $2$ is $2.5\times {10}^8{\text{ms}}^{-1}$. The critical angle for which a ray of light going from $1$ to $2$ is totally internally reflected is

A football is kicked with a velocity of 20 m/s at an angle of ${45}^{\circ }$ with the horizontal. Find the maximum height it reaches.

If $\alpha$ and $\beta$ be two roots of the equation $x^2-64x+256=0.$ Then the value of ${\left(\frac{{\alpha }^3}{{\beta }^5}\right)}^{\frac{1}{8}}+{\left(\frac{{\beta }^3}{{\alpha }^5}\right)}^{\frac{1}{8}}$ is:

A uniform rod of length $L$ is free to rotate in a vertical plane about a fixed horizontal axis through $B$. The rod begins rotating from rest from its unstable equilibrium position. When it has turned through an angle $\theta$, its average angular velocity $\omega$ is given as:

The magnitude of electric field due to an infinite uniformly charged insulating sheet is 10 N/C at a point which is at a distance 3m away from it. The surface charge density of the sheet will be?

In the figure shown $AB$ is a rod of length $30\text{cm}$ and area of cross -section $1{\text{cm}}^2$ and thermal conductivity $336\text{W/K}$. The ends $A$ and $B$ are maintained at temperature ${20}^{\circ }\text{C}$ and ${40}^{\circ }\text{C}$ respectively. The point $C$ on this rod is connected to a box $D$ containing ice at $0^{\circ }\text{C}$, through a highly conducting wire of negligible heat capacity. The rate at which ice box melts is:

The I-V characteristic of an LED is

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