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Laws Of Motion

Question
CBSEENPH11020539

A block A of mass m1 rests on a horizontal table. A light string connected to it passes over a frictionless pulley at the edge of the table and from its other end, another block B of mass m2 is suspended. The coefficient of kinetic friction between the block and the table is straight mu subscript straight k. When the block A is sliding on the table, the tension in the string is

  • fraction numerator left parenthesis straight m subscript 2 plus straight mu subscript straight k straight m subscript 1 right parenthesis straight g over denominator left parenthesis straight m subscript 1 plus straight m subscript 2 right parenthesis end fraction
  • fraction numerator left parenthesis straight m subscript 2 minus straight mu subscript straight k straight m subscript 1 right parenthesis straight g over denominator left parenthesis straight m subscript 1 plus straight m subscript 2 right parenthesis end fraction
  • fraction numerator straight m subscript 1 straight m subscript 2 left parenthesis 1 plus straight mu subscript straight k right parenthesis straight g over denominator left parenthesis straight m subscript 1 plus straight m subscript 2 right parenthesis end fraction
  • fraction numerator straight m subscript 1 straight m subscript 2 left parenthesis 1 minus straight mu subscript straight k right parenthesis straight g over denominator left parenthesis straight m subscript 1 plus straight m subscript 2 right parenthesis end fraction

Solution

C.

fraction numerator straight m subscript 1 straight m subscript 2 left parenthesis 1 plus straight mu subscript straight k right parenthesis straight g over denominator left parenthesis straight m subscript 1 plus straight m subscript 2 right parenthesis end fraction

FBD of block A,

T -m1afk ..... (i)
FBD  of block B

m2g -T = m2a ... (ii)
Adding Eqs. (i) and (ii), we get
m2g-m1a = m2a +fkrightwards double arrow space straight m subscript 2 straight g minus straight m subscript 1 straight a space equals space straight m subscript 2 straight a space plus straight f subscript straight k
rightwards double arrow space straight a equals space fraction numerator left parenthesis straight m subscript 2 minus straight u subscript straight k straight m subscript 1 right parenthesis straight g over denominator straight m subscript 1 plus straight m subscript 2 end fraction
from space equation space left parenthesis ii right parenthesis
straight T equals space straight m subscript 2 minus left parenthesis straight g minus straight a right parenthesis
equals space straight m subscript 2 open square brackets 1 minus fraction numerator left parenthesis straight m subscript 2 minus straight mu subscript straight k straight m subscript 1 over denominator straight m subscript 1 plus straight m subscript 2 end fraction close square brackets straight g
straight T equals space fraction numerator straight m subscript 1 straight m subscript 2 space left parenthesis 1 plus straight mu subscript straight k right parenthesis over denominator straight m subscript 1 plus straight m subscript 2 end fraction straight g