A heater coil is cut into two equal parts and only one part is now used in the heater. The heat generated will now be

A T shaped object with dimensions shown in the figure, is lying on a smooth floor. A force $${}^{\prime }\overrightarrow{F}{}^{\prime }$$ is applied at the point $$P$$ parallel to $$AB,$$ such that the object has only the translational motion without rotation. Find the location of $$P$$ with respect to $$C.$$

A mass $${}^{\prime }{m}^{\prime }$$ moves with a velocity $${}^{\prime }{v}^{\prime }$$ and collides inelastically with another identical mass. After collision the $$1^{st}$$ mass moves with velocity {v \over {\sqrt 3 }} in a direction perpendicular to the initial direction of motion. Find the speed of the $$2^{nd}$$ mass after collision.

The block of mass $$M$$ moving on the frictionless horizontal surface collides with the spring of spring constant $$k$$ and compresses it by length $$L.$$ The maximum momentum of the block after collision is

A body $$A$$ of mass $$M$$ while falling vertically downloads under gravity breaks into two-parts; a body $$B$$ of mass {1 \over 3} $$M$$ and a body $$C$$ of mass {2 \over 3} $$M.$$ The center of mass of bodies $$B$$ and $$C$$ taken together shifts compared to that of bodies $$B$$ and $$C$$ taken together shifts compared to that of body $$A$$ towards

If $$S$$ is stress and $$Y$$ is young's modulus of material of a wire, the energy stored in the wire per unit volume is

A $$20$$ $$cm$$ long capillary tube is dipped in water. The water rises up to $$8$$ $$cm.$$ If the entire arrangement is put in a freely falling elevator the length of water column in the capillary tube will be

The electrical conductivity of a semiconductor increases when electromagnetic radiation of wavelength shorter than $$2480$$ $$nm$$ is incident on it. The band gap in $$(eV)$$ for the semiconductor is

In a full wave rectifier circuit operating from $$50$$ $$Hz$$ mains frequency, the fundamental frequency in the ripple would be

In a common base amplifier, the phase difference between the input signal voltage and output voltage is

If a simple harmonic motion is represented by {{{d^2}x} \over {d{t^2}}} + \alpha x = 0. its time period is

The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillating bob gets suddenly unplugged. During observation, till water is coming out, the time period of oscillation would

Two simple harmonic motions are represented by the equations {y_1} = 0.1\,\sin \left( {100\pi t + {\pi \over 3}} \right) and $$y_2=0.1\cos \pi t.$$ The phase difference of the velocity of particle $$1$$ with respect to the velocity of particle $$2$$ is

The function $${\sin }^2\left(\omega t\right)$$ represents

A bullet fired into a fixed target loses half of its velocity after penetrating $$3$$ $$cm.$$ How much further it will penetrate before coming to rest assuming that it faces constant resistance to motion?

A spherical ball of mass $$20$$ $$kg$$ is stationary at the top of a hill of height $$100$$ $$m$$. It rolls down a smooth surface to the ground, then climbs up another hill of height $$30$$ $$m$$ and finally rolls down to a horizontal base at a height of $$20$$ $$m$$ above the ground. The velocity attained by the ball is

A body of mass $$m$$ is accelerated uniformly from rest to a speed $$v$$ in a time $$T.$$ The instantaneous power delivered to the body as a function of time is given by

The upper half of an inclined plane with inclination $$\varphi$$ is perfectly smooth while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom if the coefficient of friction for the lower half is given by

The self inductance of the motor of an electric fan is $$10$$ $$H$$. In order to impart maximum power at $$50$$ $$Hz$$, it should be connected to a capacitance of

The phase difference between the alternating current and $$emf$$ is {\pi \over 2}. Which of the following cannot be the constituent of the circuit?