A room 34m long is constructed to a whispering gallery. The room has an elliptical ceiling, as shown in figure. If the maximum height of the ceiling is 8m, determine where the foci are located .

A simple pendulum of length L having a bob of mass m is deflected from its rest position by an angle theta and released figure. The string hits a peg which is fixed at distance x below the point of suspension and the bob starts going in a circle centred at the peg. a. Assuming that initially the bob has a height less thasn the peg, show that the maximum height reached by the bob equals its initialheight. b. If the pendulum is released with theta=90^0 and m=L/2 find the maximum height reached by the bob above its lowest positon before the string becomes slack. c. Find the minimum value of x/L for which the bob goes in a complete circle about the pet when the pendulum is released from theta=90^0 .

A container contains water up to a height of 20 cm and there is a point source at the centre of the bottom of the container. A rubber ring of radius r floats centrally on the water. The ceiling of the room is 2.0 m above the water surface. (a) Find the radius of the shadow of the ring formed on the ceiling if r = 15 cm. (b) Find the maximum value of r for which the shadow of the ring is formed on the ceiling. Refractive index of water =4/3.

A small ball of conducting material having a charge +q and mass m is thrown upward at and angle theta to horizontal surface with an initial speed nu_(0) as shown in the figure. There exists an uniform electric field E downward along with the gravitational field g . Calculate the range maximum height and time of flight in the motion of this charged ball. Neglect the effect of air and treat the ball as a point mass .

Figure shows a smasll sphereical bal of mass m rolling down the loop track. Thebasll is released on the linear portion at a verticla height H from the lowest point. The circular part show has a radius R. a. find the kinetic energy of the ball when it is at a point where the radius makes an angle theta with the horizontal. Find the radial and the tangential accelerations of the cente when the ball is at A. c. find the bnormal force and the frictionasl force acting on the ball if H=60 cm, R=10cm theta=0 and m=70 fg.

A bob of mass 0.1 kg hung from the ceiling of room by a string 2 m long is oscillating. At its mean position the speed of a bob is 1 ms^(-1) . What is the trajectory of the oscillating bob if the string is cut when the bob is (i) At the mean position (ii) At its extreme position.

A bullet of mass 50g if fired from below into the bob of mass 450g of a long simple pendulum as shown in Fig. The bullet remains inside the bob and the bob rises through a height of 1.8m. Find the speed of the bullet.Take g=10 m/s^2

A block of mass m sliding n a smooth horizontal surface with velocity vecv meets a long horizontal spring fixed ast one end and having spring constant k as shown n figure. Find the maximum compression of the spring.

a. Obtain an expression for the mutual inductance between a long straight wire and a square loop of side a as shown in the figure. b. Now assume that the straight wire carries a current of 50 A and the loop is moved to the right with a constant velocity, v=10m//s . Calculate the induced emf in the loop at the instant when x=0.2m . Take a=0.1m and assume that the loop has a large resistance.

An electric dipole consists of charges pm 2.0 xx 10^(8) C separated by a distance of 2.0 xx 10^(-3) m. It is placed near a long ilne charge of linear charge density 4.0 xx 10^(-4) C m^(-1) as shown in figure (30-W4), Such thet the negative charge is at a distance of 2.0 cm from the line charge. Find the force acting on the dipole.