A body is thrown with a velocity of 9.8 ms^–1 making an angle of 30º with the horizontal. It will hit the ground after a time

3.0 s
2.0 s
1.5 s
1 s

Solution

Time of flight=\(\frac{2 \: usin\: \theta }{g}\)

\(=\frac{29\times 8\times sin30º}{9.8}=2\times \frac{1}{2}=1sec\)

The rate of heat flow through the cross-section of the rod shown in figure is (T₂ > T₁ and thermal conductivity of the material of the rod is K)

\(\frac{k\pi r_{1}r_{2}(T_{2}-T_{1})}{L}\)
\(\frac{k\pi (r_{1}+r_{2})^{2}(T_{2}-T_{1})}{4L}\)
\(\frac{k\pi (r_{1}+r_{1})^{2}(T_{2}-T_{1})}{L}\)
\(\frac{k\pi (r_{1}+r_{1})^{2}(T_{2}-T_{1})}{2L}\)

Solution

In producing chlorine by electrolysis 100 kW power at 125V is being consumed. How much chlorine per minute is liberated?(E.C.E. of chlorine is 0.367×10^–6 kg /C)

1.76× 10^–3kg
9.67 × 10^–3kg
17.61 × 10^–3kg
3.67 × 10^–3kg

Solution

The moment of inertia of a uniform circular disc of radius ‘R’and mass ‘M’ about an axis passing from the edge of the disc and normal to the disc is

MR²
¹⁄₂ MR²
³⁄₂ MR²
⁷⁄₂ MR²

Solution

M.I. of a uniform circular disc of radius ‘R’ and mass ‘M’ about an axis passing through C.M.and normal to the disc is

I_CM.=¹⁄₂ MR²

From parallel axis theorem

I_T = I_CM. + MR² = ¹⁄₂ MR² + MR² = ³⁄₂ MR²

Through two parallel wires A and B, 10A and 2A of currents are passed respectively in opposite directions. If the wire A is infinitely long and the length of the wire B is 2m, then force on the conductor B, which is situated at 10 cm distance from A, will be

8 × 10^–7 N
8 × 10^–5 N
4 × 10^–7 N
4 × 10^–5 N

Solution

A block rests on a horizontal table which is executing SHM in the horizontal plane with an amplitude ‘a’. If the coefficient of friction is ‘μ’, then the block just starts to slip when the frequency of oscillation is

\(\frac{1}{2\pi }\sqrt{\frac{\mu g}{a}}\)
\(\sqrt{\frac{\mu g}{a}}\)
\(2\pi \sqrt{\frac{a}{\mu g}}\)
\(\sqrt{\frac{a}{\mu g}}\)

Solution

Two parallel plate capacitors of capacitances C and 2C are connected in parallel and charged to a potential difference V.The battery is then disconnected and the region between the plates of the capacitor C is completely filled with a material fo dielectric constant K.The potential difference across the capacitors now becomes

\(\frac{3V}{K+2}\)
KV
^V⁄_K
³⁄_KV

Solution

Directions : Each question contains STATEMENT-1 and STATEMENT-2. Choose the correct answer(ONLY ONE option is correct ) from the following

Statement -1 :If dot product and cross product of \(\overrightarrow{A}\) and \(\overrightarrow{B}\) are zero, it implies that one of the vector \(\overrightarrow{A}\) and \(\overrightarrow{B}\) must be a null vector

Statement -2 :Null vector is a vector with zero magnitude.

(a)Statement -1 is false, Statement-2 is true
(b)Statement -1 is true, Statement-2 is true; Statement -2 is a correct explanation for Statement-1
(c)Statement -1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1
(d)Statement -1 is true, Statement-2 is false

Solution

(c)Statement -1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1

The work function of aluminium is 4.2 eV. If two photons,each of energy 3.5 eV strike an electron of aluminium, then emission of electrons

will be possible
will not be possible
Data is incomplete
Depends upon the density of the surface

Solution

For emission of electrons incident energy of each photon must be greater than work function(threshold energy).

A long string is stretched by 2 cm and the potential energy is V. If the spring is stretched by 10 cm, its potential energy will be

V/25
V/5
5 V
25 V

Solution

\(v=\frac{1}{2}k(x)^{2}=\frac{1}{2}k(2)^{2}\) or \(k=z\frac{2v}{4}=\frac{v}{2}\)

\(v'=\frac{1}{2}k(10)^{2}=\frac{1}{2}\times \left ( \frac{1}{2} \right )(10)^{2}=25v\)

Consider the following two statement:

I.Linear momentum of a system of particles is zero.

II.Kinetic energy of a system of particles is zero.

Then

I implies II but II does not imply I.
I does not imply II but II implies I.
I implies II and II implies I.
I does not imply II and II does not imply I.

Solution

If \(\overrightarrow{L}\) = 0 ⇒ K.E may or may not be zero.

If K.E = 0 ⇒ \(\overrightarrow{L}\) = 0.

A rifle man, who together with his rifle has a mass of 100 kg,stands on a smooth surface and fires 10 shots horizontally.Each bullet has a mass 10 g and a muzzle velocity of 800 ms^-1. The velocity which the rifle man attains after firing 10 shots is

8 m s^-1
0.8 m s^-1
0.08 m s^-1
– 0.8 m s^-1

Solution

According to law of conservation of momentum,

100 v=- ¹⁰⁄₁₀₀₀ × 10 × 800

ie, v= 0.8 ms^-1

Moment of inertia does not depend upon

distribution of mass
axis of rotation
point of application of force
None of these

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

zero
π/4
π/2
π

Solution

The phase difference between output voltage and input signal voltage in common base transistor circuit is zero

A tunnel has been dug through the centre of the earth and a ball is released in it. It executes S.H.M. with time period

42 minutes
1 day
1 hour
84.6 minutes

Solution

\(T=2\pi \sqrt{\frac{R}{g}}=2\pi \sqrt{\frac{64\times 10^{2}}{9.8}}=2\times \frac{22}{7}\times \frac{8\times 10^{3}}{7\times \sqrt{2}}\)

\(=\frac{\sqrt{2}\times 22\times 8\times 1000}{49\times 60}min =84.6\: min\)

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