May 2011 - Career Point

Ans.(C)(C)[C]100%Intensity0100%Intensity0TRTRθ 90ºθ 90º23. The density of solid ball is to be determined in anexperiment. The diameter of the ball is measuredwith a screw gauge, whose pitch is 0.5 mm andthere are 50 divisions on the circular scale. Thereading on the main scale is 2.5 mm and that onthe circular scale is 20 division. If the measuredmass of the ball has a relative error of 2%, therelative percentage error in the density is -(A) 0.9% (B) 2.4%(C) 3.1% (D) 4.2%Ans. [C]Pitch = 0.5 mmdivisions on the = 50circular scale0. 5⇒ least count of screw gauge = = 0.01 50θθWhen θ > θ C , no ray will transmit⇒ T = 0, T + R = 100 % and R > 0Tθ ce22. A wooden block performs SHM on a frictionlesssurface with frequency, v 0 . The block carries acharge + Q on its surface. If now a uniformelectric field E r is switched-on as shown, then theSHM of the block will beAns.E r +Q(A) of the same frequency and with shifted meanposition.(B) of the same frequency and with the samemean position(C) of changed frequency and with shifted meanposition(D) of changed frequency and with the samemean position[A]In order to have net force zero, the mean positionwill be shifted towards right but the time periodwill remain unaffected.main scale, reading = 2.5 mmcircular scale reading = 20⇒ reading = 2.5 mm + (20 × 0.01) mm= 2.5 mm + 0.2 mm = 2.7 mmmρ =34π ⎡D⎤3 ⎢ 2 ⎥⎣ ⎦∆ ρρ%error =∆ m ∆D= + 3m D∆ ρ × 100ρ⎛ 0.01⎞= 2 % + 3 ⎜ ⎟ × 100 = 3.1.⎝ 2.7 ⎠24. A ball of mass 0.2 kg rests on a vertical post ofheight 5m. A bullet of mass 0.01 kg. travellingwith a velocity V m/s in a horizontal direction,hits the centre of the ball. After the collision, theball and bullet travel independently. The ball hitsthe ground at a distance of 20 m and the bullet ata distance of 100 m from the foot of the post. Theinitial velocity V of the bullet isV m/sH = 5m020 100XtraEdge for IIT-JEE 85 MAY 2011