Show that the maximum safety speed` (V_max) = sqrt{(rg(mu_s+tantheta))/((1-mu_s tantheta)`

Show that the minimum angular speed necessary to keep a rider omega = sqrt(g/(mu_sR) .

Starting from rest a fan takes 5 s to attain the maximum speed of 400 rpm. Assuming constant acceleration, the time taken by the fan in attaining half the maximum speed is

On a dry road , the maximum permissible speed of car in a circular path is 12 ms^-1 . IF the road becomes wet, then the maximum speed is 4sqrt2ms^-1 . IF the coefficient of friction for dry road is mu , then that for the wet road is

Prove the following: sqrt(frac(1-cos2theta)(1+cos2theta))=tantheta

Find the most general value of theta satisfyingn the equation tantheta=-1 and costheta=(1 )/(sqrt(2)) .

Two wires shown in the figure are connected in a series circuit and the same amount of current of 10A passes through both, but in opposite directions seperation between the two wires is 8 mm. The length AB is S = 22 cm. Obtain the direction and magnetic field due to current in wire 2 on the section AB of wire 1. Also obtain the magnetic and direction of the force on wire 1. (mu_0=4pixx10^-7TmA^-1) .

When the road is dry and the coefficient of friction is mu , the maximum speed of a car in a circular path is 10 m/s. if the road becomes wet and mu'=(mu)/(2) , what is the maximum speed permitted?

What is the maximum value of the force F such that the block shown in the arrangement does not move ? (Given mu =(1)/(2sqrt3)

Show that the average speed of a particle performing S.H.M. in one oscillation is frac(2)(pi) max speed .

The coefficient of static friction, mu_(s) between block A of mass 2 kg and the table as shown in the figure is 0.2. What would be the maximum mass value of block B so that the two blocks do not move? The string and the pulley are assumed to be smooth and massless. (g=10m//s^(2))