List of practice Questions

A conducting circular loop is placed in X -Y plane in presence of magnetic field
\(\stackrel{→}{B} = (3t^3\hat{j}+3t^2\hat{k})\) in SI unit. If the radius of the loop is 1 m, the induced emf in the loop at time \(t = 2s\) is \(nπV\). The value of \(n\) is ______.

Two sources of equal emfs are connected in series. This combination is connected to an external resistance R. The internal resistances of the two sources are r₁ and r₂ (r₁ > r₂). If the potential difference across the source of internal resistance r₁ is zero, then the value of R will be :

A coil is placed in a time varying magnetic field. If the number of turns in the coil were to be halved and the radius of wire doubled, the electrical power dissipated due to the current induced in the coil would be:
(Assume the coil to be short circuited.)

A coil of inductance 1 H and resistance 100 Ω is connected to a battery of 6 V. Determine approximately :
(a) The time elapsed before the current acquires half of its steady – state value.
(b) The energy stored in the magnetic field associated with the coil at an instant 15 ms after the circuit is switched on.
(Given \(ln2=0.693\), e^–3/2 = 0.25)

A closely wounded circular coil of radius 5 cm produces a magnetic field of 37.68×10^–4 T at its center. The current through the coil is _______ A.
[Given, number of turns in the coil is 100 and \(\pi = 3.14\)]

A wire of length 314 cm carrying current of 14 A is bent to form a circle. The magnetic moment of the coil is _______ A–m². [Given \(\pi = 3.14\)]

A screw gauge of pitch $05 \,mm$ is used to measure the diameter of uniform wire of length $68 \,cm$, the main scale reading is $15\, mm$ and circular scale reading is $7$. The calculated curved surface area of wire to appropriate significant figures is :[Screw gauge has $50$ divisions on the circular scale]

A water drop of radius $1 \,cm$ is broken into $729$ equal droplets If surface tension of water is $75 \,dync / cm$, then the gain in surface energy upto first decimal place will be : [Given $\pi=314]$

If \(Z=\frac {A^2B^3}{C^4},\) then the relative error in Z will be

A silver wire has a mass \((0.6  \overset{+}{-}  0.006)\) g, radius \((0.5 \overset{+}{-} 0.005)\) mm and length \((4 \overset{+}{-} 0.04)\) cm. The maximum percentage error in the measurement of its density will be

Which of the following physical quantities have the same dimensions?

A unit scale is to be prepared whose length does not change with temperature and remains 20 cm, using a bimetallic strip made of brass and iron each of different length. The length of both components would change in such a way that difference between their lengths remains constant. If length of brass is 40 cm and length of iron will be ___ cm.

In a Vernier Calipers, 10 divisions of Vernier scale is equal to the 9 divisions of main scale. When both jaws of Vernier calipers touch each other, the zero of the Vernier scale is shifted to the left of zero of the main scale and 4th Vernier scale division exactly coincides with the main scale reading. One main scale division is equal to 1 mm. While measuring diameter of a spherical body, the body is held between two jaws. It is now observed that zero of the Vernier scale lies between 30 and 31 divisions of main scale reading and 6th Vernier scale division exactly coincides with the main scale reading. The diameter of the spherical body will be

A screw gauge of pitch 0.5 mm is used to measure the diameter of uniform wire of length 6.8 cm, the main scale reading is 1.5 mm and circular scale reading is 7. The calculated curved surface area of wire to appropriate significant figures is :
[Screw gauge has 50 divisions on its circular scale.]

In an experiment of determine the Young’s modulus of wire of a length exactly 1 m, the extension in the length of the wire is measured as 0.4 mm with an uncertainty of ±0.02 mm when a load of 1 kg is applied. The diameter of the wire is measured as 0.4 mm with an uncertainty of ±0.02 mm when a load of 1 kg is applied. The diameter of the wire is measured as 0.4 mm with an uncertainty of ± 0.01 mm. The error in the measurement of Young’s modulus (ΔY) is found to be x × 10¹⁰ Nm^–2. The value of x is ___.
(Take g=10 m/s²)

A travelling microscope is used to determine the refractive index of a glass slab. If 40 divisions are there in 1 cm on main scale and 50 Vernier scale divisions are equal to 49 main scale divisions, then least count of the travelling microscope is _______× 10^–6 m.

identical drops are charged at 22 V each. They combine to form a bigger drop. The potential of the bigger drop will be ______ V.

Two coils require 20 minutes and 60 minutes respectively to produce same amount of heat energy when connected separately to the same source. If they are connected in parallel arrangement to the same source; the time required to produce same amount of heat by the combination of coils, will be ___ min.

A body is performing simple harmonic with an amplitude of 10 cm. The velocity of the body was tripled by air jet when it is at 5 cm from its mean position. The new amplitude of vibration is \(\sqrt x\) cm_. The value of x is ___.

The variation of applied potential and current flowing through a given wire is shown in figure. The length of wire is 31.4 cm. The diameter of wire is measured as 2.4 cm. The resistivity of the given wire is measured as x × 10^–3Ω cm. The value of x is____. [Take π = 3.14]

Consider the efficiency of Carnot's engine is given by \(η=\frac {αβ}{sinθ}log_e\frac {βx}{kT}\), where \(α\) and \(β\) are constants. If \(T\) is temperature, \(k\) is Boltzman constant, \(θ\) is angular displacement and \(x\) has the dimensions of length. Then, choose the incorrect option.

The vernier constant of Vernier callipers is 0.1 mm and it has zero error of (–0.05) cm. While measuring diameter of a sphere, the main scale reading is 1.7 cm and coinciding vernier division is 5. The corrected diameter will be ________× 10^–2 cm.