Solution - Career Point

22. The displacement of interfering light waves arey 1 = 4 sin ωt and y 2 = 3 sin (ωt + π/2). The amplitudeof resultant wave is(A) 5 (B) 7 (C) 1 (D) 023. A beam of light of wavelength 600 nm from adistance source falls on a single slit 1 mm wide andresulting diffraction pattern is observed on a screen2m away. Distance between first dark fringe on eitherside of the central bright fringe.(A) 1.2 mm (B) 3.2 mm(C) 2.4 mm (D) 4.2 mm24. The intensity of light from one source is double ofthe other coherent source in a double slit experiment.The ratio of destructive to constructive interference inthe obtained pattern is(A) 34 (B) 1/34 (C) 17 (D) 1/1725. Two radioactive material of half life T are producedat different instants. Their activities area found to beA 1 and A 2 respectively when A 2 < A 1 . Their agedifference isA 2A1(A) 0.44 T log (B) 1.44 T logAAA(C) 4.44 T logA121A(D) 5.44 T logA26. Three concentric conducting spherical shell x, y and zhave radii a, b and c respectively such that c > b > a,their surface charge density are σ, –σ and σrespectively. Then potential V x is given byC22128. The potential energy of a particle varies with distanceA xx from a fixed origin as U = , where A and Bx2 + Bare dimensional constant then dimensional formulafor AB is(A) M L 7/2 T –2 (B) M L 11/2 T –2(C) M 2 L 9/2 T –2 (D) M L 13/2 T –329 A particle leaves the origin at t = 0 and moves in the+ve x axis direction. Velocity of the particle at any⎛ t ⎞instant is given by v = u ⎜1 − ⎟ . If u = 10 m/s and⎝ t´⎠t´ = 5 sec. Find the x coordinate of the particle at aninstant of 10s.vut´ = 5 sect(A) 0 (B) 10 m (C) 20 m (D) –10 m30. An aero-plane drops a parachutist. After covering adistance of 40 m, he opens the parachute and retardsat 2 ms –2 . If he reaches the ground with a speed of2ms –1 , he remains in the air for about(A)(C)σε0⎡a 2⎢⎢⎣c⎤− b + c⎥⎥⎦axyz(B)bσ [a – b + c]ε 0σ σ [a + b + c] (D) – [a + b – c]ε 0ε0(A) 16 s (B) 3 s (C) 13 s (D) 10 s31. A tank moves uniformly along x-axis. It fires a shotfrom origin at an angle of 30º with horizontal whilemoving along positive x-axis & the second shot isalso fired similarly that the tank moved alongnegative x-axis. If the respectively range of the shotsare 250 m and 200 m along x-axis, the velocity of thetank.27. A certain physical quantity is calculated from the30ºπformula (a 2 – b 2 )h, where h, a and b are all lengths.3The quantity being calculated is(A) velocity (B) length(C) area(D) volume(A) 9.4 m/s(C) 3.9 m/s(B) 4.9 m/s(D) 5.9 m/sXtraEdge for IIT-JEE 78APRIL 2010