CBSE
A fully charged capacitor C with initial charge q_{0} is connected to a coil of self inductance L at t = 0. The time at which the energy is stored equally between the electric and the magnetic fields is
A.
As initially, charge is maximum
∴ q = q_{o}cos ωt
Current,
A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heat γ.It is moving with speed v and it suddenly brought to rest. Assuming no heat is lost to the surroundings, its temperature increases by
C.
As no heat is lost, therefore,
Loss of kinetic energy = Gain of internal energy of gas
i.e.,
A boat is moving due east in a region where the earth's magnetic field is 5.0 × 10^{-5} NA^{-1}m^{-1} due north and horizontal. The boat carries a vertical aerial 2m long. If the speed of the boat is 1.50 ms^{-1}, the magnitude of the induced emf in the wire of aerial is
0.75 mV
0.50 mV
0.15 mV
1 mV
C.
0.15 mV
E_{ind} = B × v × l
= 5.0 × 10-5 × 1.50 × 2
= 10.0 × 10-5 × 1.5
= 15 × 10-5 vot.
= 0.15 mv
Water is flowing continuously from a tap having an internal diameter 8 × 10^{-3} m. The water velocity as it leaves the tap is 0.4 ms^{-1}. The diameter of the water stream at a distance 2 × 10^{-1} m below the tap is close
to:
7.5 x 10^{-3} m
9.6x 10^{-3} m
3.6x 10^{-3} m
5.0x 10^{-3} m
C.
3.6x 10^{-3} m
From Bernoulli's theorem
Three perfect gases at absolute temperature T_{1}, T_{2} and T_{3} are mixed. The masses of molecules are m_{1},m_{2} and m_{3} and the number of molecules is n_{1},n_{2} and n_{3} respectively.Assuming no loss of energy, the final temperature of the mixture is
A.
For adiabatic process i.e., no heat change
A current I flows in an infinitely long wire with cross-section in the form of a semicircular ring of radius R. The magnitude of the magnetic induction along its axis is
D.
A mass M, attached to a horizontal spring, executes SHM with an amplitude A_{1}. When the mass M passes through its mean position than a smaller mass m is placed over it and both of them move together with amplitude A_{2}. The ratio of (A_{1}/A_{2}) is
C.
At mean position, F_{net} = 0
Therefore, By conservation of linear momentum,
Mv_{1} = (M+m)v_{2}
Mω_{1}A_{1} = (M+m)ω_{2}A_{2}
⇒
Two particles are executing simple harmonic motion of the same amplitude Aand frequency ω along the x - axis. Their mean position is separated by distance X_{0} (X_{0} >A). If the maximum separation between them is (X0 + A), the phase difference between their motion is
π/3
π/4
π/6
π/2
A.
π/3
x_{1} = A sin( ωt + Φ_{1})
x_{2} = A sin( ωt + Φ_{2})
100g of water is heated from 30°C to 50°C ignoring the slight expansion of the water, the change in its internal energy is (specific heat of water is 4184 J/Kg/K)
8.4 kJ
84 kJ
2.1 kJ
4.2 kJ
A.
8.4 kJ
ΔQ = M,S,ΔT
= 100 × 10^{-3} × 4.184 × 20 = 8.4 × 10^{3}
ΔQ = 84 kJ, ΔW = 0
ΔQ = ΔV + ΔW
ΔV = 8.4 kJ
A Carnot engine operating between temperatures T_{1} and T_{2} has efficiency 1/6. When T_{2} is lowered by 62 K, its efficiency increases to 1/3. Then T_{1} and T_{2} are, respectively
372 K and 330 K
330 K and 268 K
310 K and 248 K
372 K and 310 K
D.
372 K and 310 K
The efficiency is given by,