In a submarine telegraph cable the speed of signaling varies as `x^2log(1/x)` where `x` is the ratio of the radius of the cable to that of covering. Then the greatest speed is attained when this ratio is

If the radii of circular path of two particles are in the ratio of 1 :2 , then in order to have same centripetal acceleration, their speeds should be in the ratio of :

If y varies directly as x and y=12, where x=c, what is y in terms of c when x=8 ?

lim_(xrarr oo) (log[x])/(x) , where [x] denotes the greatest integer less than or equal to x, is

The earth moves around the Sun in an elliptical orbit as shown in Fig. The ratio OA//OB=x . The ratio of the speed of the earth at B to that at A is nearly

The ratio of the speed of a projectile at the point of projection to the speed at the top of its trajectory is x. The angle of projection with the horizontal is

Find the domain of the function f(x)=log_(e)(x-[x]) , where [.] denotes the greatest integer function.

The equation of a travelling sound wave is y = 6.0 sin (600 t - 1.8 x) where y is measured in 10^-5m , t in second and x in metre. (a) Find the ratio of the displacement amplitude of the particles to the wavelength of the wave. (b) Find the ratio of the velocity amplitude of the particles to the wave speed.

Find the domain and range of f(x)=log[ cos|x|+1/2] ,where [.] denotes the greatest integer function.

A projectile attains a certain maximum height H1 when projected from earth. If it is projected at the same angle and with the same initial speed from the moon, where the acceleration due to gravity is one-sixth that on earth, the maximum height attended by the projectile is H_2 . THe ratio H_2//H_1 is:

A flexible steel cable of total length L and mass per unit length mu hangs vertically from a support at one end. (a) Show that the speed of a transverse wave down the cable is v =sqrtg(L - x) , where x is measured from the support. (b) How long will it takes for a wave to travel down the cable?