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JIPMER 2006
Exam
JIPMER
Year
2006
Subject
Physics
Chapter
Laws of Motion

JIPMER 2006 · Physics · Laws of Motion

Two weights w_1 and w_2 are suspended to the two strings on a...

Two weights w1w_1 and w2w_2 are suspended to the two strings on a frictionless pulley. When the pulley is pulled up with an acceleration gg, then the tension in the string is :Two weights w_1 and w_2 are suspended to the two strings on a frictionless pulley. When the pulley is pulled up with an

Options

  1. A4w1w2w1+w2\frac{4 w_1 w_2}{w_1+w_2}
  2. Bw1w2w1+w2\frac{w_1 w_2}{w_1+w_2}
  3. C2w1w2w1+w2\frac{2 w_1 w_2}{w_1+w_2}
  4. Dw1+w22\frac{w_1+w_2}{2}

Correct answer

A. 4w1w2w1+w2\frac{4 w_1 w_2}{w_1+w_2}

Step-by-step solution

Equation of motion for first weight Two weights w_1 and w_2 are suspended to the two strings on a frictionless pulley. When the pulley is pulled up with an T−m1g=m1(g+a)⇒T−2m1g=m1a…(1)\begin{aligned} T-m_1 g & =m_1(g+a) \\ \Rightarrow \quad T-2 m_1 g & =m_1 a\ldots(1)\end{aligned} For second weight m2g−T=m2(a−g)2m2g−T=m2a…(2)\begin{aligned} m_2 g-T & =m_2(a-g) \\ 2 m_2 g-T & =m_2 a\ldots(2)\end{aligned} On solving Eqs. (1) and (2) T=4m1m2g(m1+m2)=4w1w2(w1+w2)\begin{aligned} T & =\frac{4 m_1 m_2 g}{\left(m_1+m_2\right)} \\ & =\frac{4 w_1 w_2}{\left(w_1+w_2\right)}\end{aligned}
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