Show that the projection angle `thetha_0` for a projectile launched from the origin is given by `theta_0 =tan^1(4h_m//R)`
Where the symbols have their usual meaning.

(Attempt any nine of the following questions)A current carrying solenoid is shown be low. Show that the magnetic field intensity at point P be B= mu_0/(4pi) (2m)/r^3 Where the symbols have their usual meaning.

The equations of light wave from two sources are y_1=a_1sinomegat and y_2=a_2sin(omegat+phi) where the symbols have their usual meaning. The individual intesities are I_1 and I_2 . Show that the minimum resultant intesity due to superposition is I_(min)=I_1+I_2-2sqrt(I_1I_2) .

Show that the relation R in the set of integers given by R={(a,b):4" divides "a-b} is an equivelence relation. Find the set of all elements related to 0.

The potential energy function for a particle executing linear simple harmonic motion is given by V(x) =kx^2/2, where k is the force constant of the oscillator. For k = 0.5 N ^-1 , the graph of V(x) versus x is shown in Fig. 6.12. Show that a particle of total energy 1 J moving under this potential must ‘turn back’ when it reaches x = ± 2 m.,br>

From a window h m high above the ground in a street, the angles of elevation and depression of the top and foot of the other house on the opposite side of the street as alpha and beta respectively show that height of the opposite house is h(1+tan alpha cos beta)m .

A bob of mass 0.1 kg hung from the ceiling of a room by a string 2 m long is set into oscillation. The speed of the bob at its mean position is 1 m s^1. What is the trajectory of the bob if the string is cut when the bob is (a) at one of its extreme positions, (b) at its mean position.