May 2011 - Career Point

40. A block is moving on an inclined plane makingan angle 45º with the horizontal and thecoefficient of friction is µ. The force required tojust push it up the inclined plane is 3 times theforce required to just prevent it from slidingdown. If we define N = 10 µ, then N is.Ans. [5]Sol.45ºN=mgcosθmgsinθ + µmgcosθ = 3(mgsinθ – µmgcosθ)1 µ 3 3µ⇒ + = −2 2 2 2⇒4µµ = 212=22⎛ 1 ⎞N = 10µ = 10 ⎜ ⎟ = 5⎝ 2 ⎠41. A boy is pushing a ring of mass 2 kg and radius0.5 m with a stick as shown in the figure. Thestick applies a force of 2 N on the ring and rolls itwithout slipping with an acceleration of 0.3 m/s 2 .The coefficient of friction between the groundand the ring is large enough that rolling alwaysoccurs and the coefficient of friction between thestick and the ring is (P/10). The value of P is.StickAns. [4]Sol.mgGroundf 22NP×2 Pf 1 = µ×2 = =10 52 – f 2 = Ma cm …….(1)f 2 = 2 – 2 × 0.3 = 1 .4 N(f 2 – f 1 ) R = I cm αa(f 2 – f 1 ) R = MR2 cm×Rf 2 – f 1 = Ma cmf 1 = f 2 – ma cm = 1.4 – 2 × 0.3 = 0.8 NP0 .8 = ⇒ P = 45Note : It has been assumed that the stick applieshorizontal force of 2N (only normal reaction)42. Four point charge, each of +q, are rigidly fixed atthe four corners of a square planar soap film ofside 'a'. The surface tension of the soap film is γ.The system of charges and planar film are inequilibrium, andAns. [3]Sol.⎡2q ⎤a = k ⎢ ⎥⎦⎣ γF AC1/NF AB, where 'k' is a constant. Then N is.F +qADA+qDF AC =BC+q +qq28πεa0F AD = F AB =F R =⇒ a 3 =22q24πεa0q ⎛ 1 ⎞⎜2cos45º+ ⎟24πε0a⎝ 2 ⎠= r (2) (BD) = 2 r( 2 a)2⎛q ⎜⎝8⎛2q ⎞a = k⎜⎟r⎝ ⎠1/3⎛ 1 ⎞⎜ 2 + ⎟where k = ⎜ 2 ⎟⎜ 8 2π⎟⎝ ⎠21 ⎞2 + ⎟2 ⎠2πεr1/30⇒ N = 3XtraEdge for IIT-JEE 72 MAY 2011