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A positive charge +Q is fixed at a poibt A. Another positively charged particle of mass m and charge +q is projected from a point B with velocity u as shown in (Fig. 3.103). Point B is at a large distance from A and at distance d from the line A C. The initial velocity is parallel to the line A C. The point C is at a very large distance from A. Find the minimum distance (in meter) of +q from +Q during the motion. Take Q q = 4 pi epsilon_0 m u^2 d and d (sqrt(2) - 1) m . .

Supose directioncoisnes of two lines are given by u l+vm+wn=0 and al^2+bm^2+cn^2=0 where u,v,w,a,b,c are arbitrary constnts and l,m,n are directioncosines of the lines. For u=v=w=1 directionc isines of both lines satisfy the relation. (A) (b+c)(n/l)^2+2b(n/l)+(a+b)=0 (B) (c+a)(l/m)^2+2c(l/m)+(b+c)=0 (C) (a+b)(m/n)^2+2a(m/n)+(c+a)=0 (D) all of the above

A B C D is a quadrilateral. A line through D , parallel to A C , meets B C produced in P as shown in Figure. Prove that a r\ ( A B P)=a r\ (Q u a ddotA B C D)dot

The element curium _96^248 Cm has a mean life of 10^13s . Its primary decay modes are spontaneous fission and alpha -decay, the former with a probability of 8% and the later with a probability of 92%, each fission releases 200 MeV of energy. The masses involved in decay are as follows _96^248 Cm=248.072220 u , _94^244 P_u=244.064100 u and _2^4 He=4.002603u . Calculate the power output from a sample of 10^20 Cm atoms. ( 1u=931 MeV//c^2 )

Two particles A and B having charges of +2.00 xx 10^(-6) C and of - 4.00xx 10^(-6) respectively are held fixed at a separation of 20.0 cm . Locate the point(s) on the line AB where (a) the electric field is zero (b) the electric potential is zero.

2.00 mol of a monatomic ideal gas (U=1.5nRT) is enclosed in an adiabatic, fixed , vertical cylinder fitted with a smooth, light adiabatic piston.the piston is connected to a vertical spring of spring constant 200 N m^(-1) as shown in .the area of cross section of the cylinder is 20.0 cm^(2) . initially, the spring is at its natural length and the temperature of the gas is at its natural length and the temperature of the gas is 300 K. the atmosphere pressure is 100 kPa. the gas is heated sloewly for some time by means of an electric heater so as to move the poston up through 10 cm. find (a) the work done by the gas (b) the final temperature of the gas and (c ) the heat supplied by the heater.

Three balls A, B and C of same mass m are placed on a frictionless horizontal plane in a straight line as shown. Ball A is moved with velocity u towards the middle ball B . If all the collisions are elastic, find the final velocities of all the balls.