An electric lamp is connected to 220 V, 50 Hz supply. Then the peak value of voltage is
Answer :- c
Solution :- V(0) = Vrms × 2
= 220 × √2
In a step-up transformer the voltage in the primary is 220 V and the current is 5A. The secondary voltage is found to be 22000V. The current in the secondary (neglect losses) is
A body moves along a circular path of radius 10 m and the coefficient of friction is 0.5. What should be the angular velocity of the body, if it is not to slip on the surface?
A semi circle arc of radius 'a' is charged uniformly and the charge per unit length is λ. The electric field at its centre is
A gun fires the bullets each of mass 10 g with a velocity of 50 m−s-1. If 1000 bullets are fired per second, then thrust on the shoulder will be
An electric dipole is placed along the X-axis at the origin O. A point P is at a distance of 20 cm from this origin such that OP makes an angle π/3 with the X axis. If electric field at P makes an angle θ with X-axis, the value of θ is
A metre stick AB hinged (without friction) at the end A as shown in the figure is kept horizontal by means of a string tied to the end B, the other end of the string being tied to a hook. The string is carefully cut (or burnt), and the scale executes angular oscillations about an axis passing through the end A. What is the speed of the end B when the metre stick assumes vertical position immediately after the string is burnt? (Acceleration due to gravity = 10 ms–2)
The centre of gravity of the metre stick is at its middle. When the string is burnt, the height of the centre of gravity is reduced by 0.5 m, thereby reducing the gravitational potential energy of the metre stick by Mgh= M×10×0.5 = 5M joule, where M is the mass of the metre stick.
The decrease in the potential energy is equal to the increase in kinetic energy. Therefore in the vertical position of the metre stick, its kinetic energy
(½)Iω2 = 5M
Since the moment of inertia of a uniform bar of length L about a normal axis through ite mid point is ML2/12, its moment of inertia about a parallel axis through its end is ML2/3. [You will get this by applying the parallel axis theorem (see the post dated 2oth January 2008)]
Therefore, we have (½)(ML2/3)ω2 = 5M
Since ω = v/L and L = 1 metre, the above equation becomes
v2/6 = 5, from which v = √30 = 5.4 ms–1 (approximately).
The symbolic representation of four logic gates are given below:
The logic symbols for OR, NOT and NAND gates are respectively:
If a long hollow copper pipe carries a current then magnetic field produced will be
Two bodies of mass 10 kg and 5 kg moving in concentric orbits of radii R and r such that their periods are the same. Then the ratio between their centripetal acceleration is
The internal energy of the gas increases when
When a gas expands adiabatically, it loses internal energy equal to the work done by the gas. In this case the temperature of the gas decreases.
When a gas is compressed adiabatically, it gains internal energy equal to the work done on the gas. In this case the temperature of the gas increases.
The dimensional equation for magnetic flux is
If T is the reverberation time of an auditorium of volume V, then
Generally reverberation time is proportional to linear dimensions of the room. Hence, it will be proportional to the volume of the room.
The figure shows an energy level diagram for the hydrogen atom. Several transition are marked as I, II, III,........ . The diagram is only indicative and not to scale.
Q. The wavelength of the radiation involved in transition II is -
The orbital velocity of an artificial satellite in a circular orbit just above the earth’s surface is v0. The orbital velocity of satellite orbiting at an altitude of double the radius of earth is V0/√n Then the value of n is :
A 300 W carrier is modulated to a depth 75%. The total power in the modulated wave is:-
A conducting rod of 1 m length and 1 kg mass is suspended by two vertical wires through its ends. An external magnetic field of 2T is applied normal to the rod. Now, the current to be passed through the rod so as to make the tension in the wires zero is : (Take g = 10 ms–2) :-
Magnetic force on rod = BIℓ
Weight of the rod = mg
For no tension in wire, BIℓ = mg
At what speed a ball must be projected vertically upward so that distance travelled by it in 5th second is equal to distance travelled in sixth second (in m/s):-
time of flight = (5 sec) × 2 = 10 sec
µ = gt = 9.8 × 5 = 49 m/s
In thermodynamic process pressure of a fixed mass of gas is changed in such a manner that the gas releases 30 joule of heat and 18 joule of work was done on the gas. If the initial internal energy of the gas was 60 joule, then, the final internal energy (in J) will be:
ΔQ = –30J
Δw = –18
Ui = 60 J
Uf = ?
ΔQ = Δw + Uf – Ui
–30 = –18 + Uf – 60 ⇒ Uf = 48 J