A nucleus is at rest in the laboratory frame of reference. Show that if it disintegrates into two smaller nuclei the products must move in opposite directions.

A and B are two points of 150 km apart on a highway. A car starts from A and another from B at the same time. If they move in the same direction, they meet in 15 hours, but if they move in opposite direction, they meet in one hour. Find their speeds.

The binding energy of a H-atom, considering an electron moving around a fixed nucleus (proton), is B=-(me^4)/(8n^2epsilon_0^2h^2) (m=electron mass) If one decides to work in a frame of reference where the electron is at rest, the proton would be moving around it. By similar arguments, the binding energy would be B=-(me^4)/(8n^2epsilon_0^2h^2) (M=proton mass). This last expression is not correct because.

Deutron is a bound state of a nuetron and a proton with a binding energy B=2.2 MeV. A gamma-rays of energy E is aimed at a deuteron nucleus to try to break it into a (neutron+proton) such that the n and p move in the direction of the incident gamma-rays . If E=B, show that this cannot happen. Hence calculate how much bigger than B must E be for a such a process to happen.

Two particles, each of mass mand speed v, travel in opposite directions along parallel lines separated by a distance d. Show that the vector angular momentum of the two particle system is the same whatever be the point about which the angular momentum is taken.

There are 2n guests at a dinner party. Supposing that eh master and mistress of the house have fixed seats opposite one another and that there are two specified guests who must not be placed next to one another, show that the number of ways in which the company can be placed is (2n-2!)xx(4n^2-6n+4)dot

A conducting rod PQ of length 20 cm and resistance 0.1 Omega rests on two smooth parallel rqails of negligible resistance AA' and CC'. It can slide on the rails and the arrangement is positioned betwaeen the poles of a permanent magnet producing unifrom magnetic field B=0.4 T. The rails, the rod and the magneitc field are in the three mutually perpendicular directions as shown in the figure. if hte ends A and C of the rails are short cicuited, find the External force required to move the rod with uniform velocity v=10cm/s.

A conducting rod PQ of length 20 cm and resistance 0.1 Omega rests on two smooth parallel rqails of negligible resistance AA' and CC'. It can slide on the rails and the arrangement is positioned betwaeen the poles of a permanent magnet producing unifrom magnetic field B=0.4 T. The rails, the rod and the magneitc field are in the three mutually perpendicular directions as shown in the figure. if hte ends A and C of the rails are short cicuited, find the Power required to move the rod with velocity v= 10 cm/s

Figure shows a metal rod PQ resting on the smooth rails AB and positioned between the poles of a permanent magnet. The rails, the rod, and the magnetic field are in three mutual perpendicular directions. A galvanometer G connects the rails through a switch K. Length of the rod =15 cm, B = 0.50 T, resistance of the closed loop containing the rod = 9.0 mOmega . Assume the field to be uniform and the rod is moved with a speed of 12 cm/s. How much power is dissipated as heat in the closed circuit? What is the source of this power? :