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Question 34

What is Joule’s heating effect? How can it be demonstrated experimentally? List its four applications in daily life.

The convex reflecting surface (silvered on the right side) is represented by the equation $2x=y^2$ as shown in figure. A ray travelling horizontally along positive x-axis becomes vertical after reflection The co-ordinates of the point of incidence can be

Two racing cars of masses $m_1$ and $m_2$ are moving in circles of radii $r_1$ and $r_2$ respectively. Their speeds are such that each makes a complete circle in the same duration of time t. The ratio of the angular speed of the first to the second car is

Two infinite length wires carries currents 8A and 6A respectively and placed along X and Y-axis. Magnetic field at a point P(0,0,d)m will be

Evaluate $\int x^2{e}^{x}dx$

Heat energy dissipated across a conductor carrying current I connected to an unknown resistance R for a time t is H.

Calculate the value of resistance R in terms of other parameters.

A pendulum clock keeps correct time at $0^{\circ }C$. Its mean coefficient of linear expansions is $\alpha {/}^{\circ }C$, then the loss, in seconds, per day by the clock if the temperature rises by $t^{\circ }C$ is -

How to justify that the rest mass of a photon is zero?

Find the MOI of four identical solid spheres about axis $X{X}^{\prime }$ placed in horizontal plane each of mass $M$ and radius $R$ as shown in figure. Line $X{X}^{\prime }$ touches two spheres (3 and 4) and passes through diameter of other two spheres (1 and 2).

In the arrangement shown in figure, $m_A=2\text{kg}$ and $m_B=1\text{kg}$. String is light and inextensible. The acceleration of centre of mass of both the blocks is

(Neglect friction)

Two condensers, one of capacity $C$ and the other of capacity $\frac{C}{2}$, are connected to a $V$-volt battery as shown.

A block of mass 1.2 kg moving at a speed of 20 cm/s collides head-on with a similar block kept at rest. The coefficient of restitution is $\frac{3}{5}$. Find the loss of kinetic energy during the collision.

In the NCERT textbook the formula for stopping distance is given as d= -v/2a.here in this equation a is decelaration right.so a must be negative.therefore the actual equation must be d=v/2a .But why is d negative.even in general the displacement in that case can't be negative since the car will be still moving forward.pls explain in detail

A particle of mass $3\text{kg}$ has been acted upon by a force $F\left(\text{N}\right)$ whose variation with time $\left(\text{s}\right)$ is shown in the figure.





If the particle is moving along a straight line with initial velocity of $4\text{m/s}$, then find the final velocity of the particle.

A closed thin walled tube has thickness, t, mean enclosed area within the boundary of the centreline of tube's thickness, $A_m$, and shear stress $\tau$. Torsional moment of resistance, T of the section would be

A $40\mu \text{F}$ capacitor is connected to a $200\text{V},50\text{Hz}$ AC supply. The RMS value of the current in the circuit is nearly

Find the position vector of the centre of mass ${\overrightarrow{r}}_{\text{com}}$ of an asymmetric uniform bar of negligible area of cross-section, shown in the figure given below.

A capacitor of capacitance $10\mu \text{F}$ is charged by connecting it to a battery of emf $5\text{V}$. The capacitor is now disconnected and reconnected to the battery with the polarity reversed. Find heat developed in the connecting wires.

The graph of $ln\frac{R}{R_0}$ versus ln A (R radius of a nucleus and A - its mass number) is

For the lens arrangement shown in the figure, The effective focal length is $-60\text{m}$. The radii of curvature of the curved surfaces of plano-convex lenses are $12\text{cm}$ each and refractive index of the material of the lens is $1.5$. Find the refractive index of the liquid.

A magnetic needle of length $l$ and poles of pole strength $\pm m$ is attached to a wooden bar of length $L$ as shown in figure and placed in a uniform magnetic field of intensity $B$. The bar and needle can revolve around point $\text{O}$. Find the magnitude of the moment of force that will cause the rotation of the bar around point $\text{O}$ if the bar makes an angle $\alpha$ with the direction of the lines of force of the magnetic field.

A concave mirror of focal length $f$ (in air) is immersed in water $(\mu =\frac{4}{3})$. The focal length of the mirror in water will be

If a spring of spring constant $k$ extends by $x$ on loading due to an applied force $F$, then the energy stored by the spring is

A water surfer is moving at a speed of 15 m/s. When he is surfing in the direction of wave, he swingsupwards every 0.8 s because of wave crests. While surfing in opposite direction to that of wave motion, he swings upwards every 0.6 s. Determine the wavelength of transverse component of the water wave.

A force of $30\text{N}$ is sufficient just to pull a block of mass $4\text{kg}$, horizontally over a flat rough surface. The angle of friction is

When a wheel completes $2000$ revolutions to cover $15\text{km}$ distance, then the radius of the wheel is?

An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass $M$. The piston and cylinder have equal cross sectional area $A$. When the piston is in equilibrium, the volume of the gas is $V_0$ and its pressure is $P_0$. The piston is slightly displaced from the equilibrium position and released. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frequency

A new unit of length is chosen such that the speed of light in vaccum is unity. What is the distance between the sun and the earth in terms of the new Unit if light takes 8 minutes and 20 second to cover the distance?

A circular disc of radius ${}^{\prime }{r}^{\prime }$ and mass ${}^{\prime }{m}^{\prime }$ is rotating about an axis passing through its COM perpendicular to its plane with an angular speed $\omega$. If the radius of the disc is halved and the angular speed is doubled, which of the following options is correct?

1. 97.23

Find the flux of the electric field through a spherical surface of radius $R$ due to a charge of ${10}^{-7}\text{C}$ at the centre and another equal charge at a point $2R$ away from the centre.

(Take ${ϵ}_o=9\times {10}^{-12}{\text{C}}^2/{\text{N-m}}^2$ )

The energy of a network in Laplace domain is given by,

the initial and the final value of the instantaneous power are respectively

$E\left(s\right)=\frac{(s+4)}{s(s+1)(s+3)}$