Two mass M and m are connected at ywo ends of an inextensible string. The string passes over a smooth frictionless pulley. Obtain the expression for acceleration of the masses and the tension in the string. Given M>m.

Asked by rakeshprasad1112 | 2nd Dec, 2016, 09:54: PM

Expert Answer:

For mass m, the forces are given as
 
T - mg = ma                                                 ...... (1)
 
Similarly, for mass M, the forces are given as
 
Mg - T = Ma                                                 ...... (2)
 
From equation (1), we have
 
T = mg + ma                                                 ...... (3)
 
Substituting equation (3) in (2) we get
 
Mg - mg - ma = Ma
g(M - m) = a(M + m)
 
begin mathsize 12px style therefore straight a equals open parentheses fraction numerator straight M minus straight m over denominator straight M plus straight m end fraction close parentheses straight g end style
 
Substituting the value of a in equation 1,
 
begin mathsize 12px style straight T equals straight m cross times open parentheses fraction numerator straight M minus straight m over denominator straight M plus straight m end fraction close parentheses straight g plus mg
therefore straight T equals fraction numerator Mm minus straight m squared over denominator straight M plus straight m end fraction straight g plus mg
therefore straight T equals straight g open parentheses fraction numerator Mm minus straight m squared over denominator straight M plus straight m end fraction plus straight m close parentheses equals straight g open parentheses fraction numerator Mm minus straight m squared plus straight m squared plus Mm over denominator straight M plus straight m end fraction close parentheses equals straight g open parentheses fraction numerator 2 Mm over denominator straight M plus straight m end fraction close parentheses end style

Answered by Romal Bhansali | 5th Dec, 2016, 10:34: AM

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