charge cloud of length `L=0.1m` ,change density `rho=3C/m^(3)` crosses a plane perpendicularly with a velocity `v=0.01m/s` .The current density is

At constant pressure the r.m.s. velocity c is related to density d as

Four identical positive point charges Q are fixed at the four corners of a square of side length l . Another charged particle of mass m and charge +q is projected towards centre of square from a large distance along the line perpendicular to plane of square. The minimum value of initial velocity v_(0) (in m/s) required to cross the square is ? (m = 1 gm, l = 4 sqrt(2) m, Q =1 mu c, q = 0.5 muc)

A steel ball of radius 2 xx 10^(-3) m is released in an oil of viscosity 0.232 Ns m^(-2) and density 840 kg m^(-3) . Calculate the terminal velocity of ball. Take density of steel as 7800 kg m^(-3)

A glass of radius 10^(-3) and density 2000 kg m^(-3) fall in a jar filled with oil of density 800 kg m^(-3) .The terminal velocity is found to be 1 cm/s. Calculate the coefficient of viscosity of oil

A conducting rod of length L=0.1 m is moving with a uniform sped v=0.2m//s on conducting raisli a magnetic field B=0.5T as shown. On one side, the end of the rails is connected to a capacitor of capacitance C=20muF . Then, the charge on the capacitor's plates are

A cylindrical conductor of diameter 0.1 mm carries a current of 90 ma. The current density (in A m^(-2) ) is (pi~~3)

A liquid of density rho=1000kg//m^(3) viscosity eta=0.1 Ns//m^(2) is flowing down in vertical pipe of large cross section. A small ball of density rho_(0)=100 kg//m^(3) and r=5cm will be at rest in flowing liquid, if velocity of flowing liquid is 10 k m//s . Then find the value of k .

A rod of mass m = 2kg , length l = 1m , has uniform cross-section area A = (8)/(3)xx10^(-3)m^(2) but its density is non-uniform. It is hinged about one end kept in water of density rho_(w) = 10^(3)kg//m^(3) . At the equilibirum, the rod becomes horizontal. Then (g=10 m//s^(2)) . Choose the correct option(s) :

The figure shown a pipe of uniform cross-section inclined in a vertical plane. A U-tube manometer is connected between the point A and B. If the liquid of density rho_(0) flows with velocity v_(0) in the pipe. Then the reading h of the manometer is

A closed of length l containing a liquid of variable density rho(x)=rho_(0)(1+alphax) find the net force exerted by the liquid on the axis of rotation. (take the cylinder to be massless and A= cross sectional area of cylinder) (a). rho_(0)Aomega^(2)l^(2)[(1)/(2)+(1)/(3)alphal] (b). rho_(0)Aomega^(2)l^(2)[(1)/(2)+(2)/(3)alphal] (c). rho_(0)Aomega^(2)l^(2)[(1)/(2)+alphal] (d). rho_(0)Aomega^(2)l^(2)[(1)/(2)+(4)/(3)alphal]