Three concentric spherical shells have radii a, b and c (a < b < c) and have surface charge densities σ, −σ and σ respectively. If VA, VB and VC denote the potentials of the three shells, then, for c = a+b, we have
The soft-iron is a suitable material for making an electromagnet. This is because soft-iron has:
A ball is projected from the bottom of an inclined plane of inclination 30o, with a velocity of 30 m s−1, at an angle of 30o with the inclined plane. If g = 10 ms−2, then the range of the ball on given inclined plane is
A capacitor of capacitance C1 is charged by connecting it to a battery. The battery is then removed and this capacitor is connected to a second uncharged capacitor of capacitance C2. If the charge gets distributed equally on the two capacitors, then the ratio of the total energy stored in the capacitors, after connection to the total energy stored in them before connection, is
A copper block of mass 5.0 kg is heated to a temperature of 500°C and is placed on a large ice block. What is the maximum amount of ice that can melt?
[Specific heat of copper: 0.39 J g-1°C-1 and latent heat of fusion of water: 335 J g-1]
A block of mass 10 kg starts sliding on a surface with an initial velocity of 9.8 ms-1. The coefficient of friction between the surface and block is 0.5. The distance covered by the block before coming to rest is [use g = 9.8 ms-2]
A long solenoid of radius R carries a time (t) - dependent current I(t) = I0t(1 - t). A ring of radius 2R is placed co-axially near its middle. During the time interval 0 ≤ t ≤ 1, the induced current (IR) and the induced EMF(VR) in the ring change as
Mass per unit area of a circular disc of radius a depends on the distance r from its centre as σ (r) = A + Br. The moment of inertia of the disc about the axis, perpendicular to the plane and passing through its centre is:
Two moles of HI was heated in a sealed tube at 440 oC till the equilibrium was reached. HI was found to be 22% decomposed. The equilibrium constant for dissociation is
If the standard electrode potential of Cu2+/Cu electrode is 0.34 V, what is the electrode potential at 0.01 M concentration of Cu2+? (T = 298K)
A reversible reaction is said to have attained equilibrium, when
100cc of 0.1M HCl and 100cc of 0.1 M NaOH solutions are mixed in a calorimeter. If the heat liberated is 'Q' kcal, the heat of neutralization ( Δ H ) (in kcal) of HCl(aq) and NaOH(l) is
In the presence of acid, the hydrolysis of methyl cyanide gives
The points (5,-4,2),(4,-3,1),(7,-6,4),(8,-7,5) are vertices of a
If the planes x+2y+Kz=0 and 2x+y-2z=0 are at right angles, then the value of K is
Each coefficients in the equation ax2+bx+c=0 is determined by throwing an ordinary die. The probability that the equation will have equal roots is
The standard deviation of 25 numbers is 40. If each of the numbers is increased by 5, then the new standard deviation will be
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