The nagative $$Zn$$ pole of a Daniell cell, sending a constant current through a circuit, decreases in mass by $$0.13g$$ in $$30$$ minutes. If the electrochemical equivalent of $$Zn$$ and $$Cu$$ are $$32.5$$ and $$31.5$$ respectively, the increase in the mass of the positive $$Cu$$ pole in this time is

The thermo $$e.m.f.$$ of a thermo -couple is $$25$$ $$\mu V/{}^{\circ }C$$ at room temperature. A galvanometer of $$40$$ $$ohm$$ resistance, capable of detecting current as low as $$10^{-5}A,$$ is connected with the thermo couple. The smallest temperature difference that can be detected by this system is

The length of a wire of a potentiometer is $$100$$ $$cm$$, and the $$e.$$ $$m.$$ $$f.$$ of its standard cell is $$E$$ volt. It is employed to measure the $$e.m.f.$$ of a battery whose internal resistance in $$0.5\Omega .$$ If the balance point is obtained at $$1=30$$ $$cm$$ from the positive end, the $$e.m.f.$$ of the battery is where $$i$$ is the current in the potentiometer wire.

An ammeter reads upto $$1$$ ampere. Its internal resistance is $$0.81$$ $$ohm$$. To increase the range to $$10$$ $$A$$ the value of the required shunt is

Consider the following two statements : $$A.$$ Linear momentum of a system of particles is zero $$B.$$ Kinetic energy of a system of particles is zero. then

According to Newton's law of cooling, the rate of cooling of a body is proportional to $${\left(\Delta \theta \right)}^n,$$ where $$\Delta \theta$$ is the difference of the temperature of the body and the surrounding, and $$n$$ is equal to :

A strip of copper and another of germanium are cooled from room temperature to $$80K.$$ The resistance of

The difference in the variation of resistance with temperature in a metal and a semiconductor arises essentially due to the difference in the

In the middle of the depletion layer of a reverse- biased $$p$$-$$n$$ junction, the

A mass $$M$$ is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes $$SHM$$ of time period $$T.$$ If the mass is increased by $$m.$$ the time period becomes {{5T} \over 3}. Then the ratio of {{m} \over M} is

Two particles $$A$$ and $$B$$ of equal masses are suspended from two massless springs of spring of spring constant $$k_1$$ and $$k_2$$, respectively. If the maximum velocities, during oscillation, are equal, the ratio of amplitude of $$A$$ and $$B$$ is

The length of a simple pendulum executing simple harmonic motion is increased by $$21\%$$. The percentage increase in the time period of the pendulum of increased length is

A body executes simple harmonic motion. The potential energy $$(P.E),$$ the kinetic energy $$(K.E)$$ and total energy $$(T.E)$$ are measured as a function of displacement $$x.$$ Which of the following statements is true ?

The displacement of particle varies according to the relation $$x=4$$$$\left(\cos \pi t+\sin \pi t\right).$$ The amplitude of the particle is

A spring of spring constant $$5\times 10^{3}N/m$$ is stretched initially by $$5$$ $$cm$$ from the unstretched position. Then the work required to stretch it further by another $$5$$ $$cm$$ is

A wire suspended vertically from one of its ends is stretched by attaching a weight of $$200N$$ to the lower end. The weight stretches the wire by $$1$$ $$mm.$$ Then the elastic energy stored in the wire is

A body is moved along a straight line by a machine delivering a constant power. The distance moved by the body in time $${}^{\prime }{t}^{\prime }$$ is proportional to

The core of any transformer is laminated so as to

In an oscillating $$LC$$ circuit the maximum charge on the capacitor is $$Q$$. The charge on the capacitor when the energy is stored equally between the electric and magnetic field is

Consider telecommunication through optical fibres. Which of the following statements is not true?