Two bodies of masses m1 and m2 are connected by a light string which passes over a frictionless, massless pulley. If the pulley is moving upward with uniform acceleration (g/2), then tension in the string will be

Question

Two bodies of masses m1 and m2 are connected by a light string which passes over a frictionless, massless pulley. If the pulley is moving upward with uniform acceleration (g/2), then tension in the string will be (A) (3 m1 m2/m1+m2) g (B) (m1+m2/4 m1 m2) g (C) (2 m1 m2/m1+m2) g (D) (m1 m2/m1+m2) g

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/660707b2cf8fa9dcccf0cb1d5659f410-.png" /> Writing equation from the reference frame of pulley (3 m1 g/2)-T=m1 a ...(i) T-(3 m2 g/2)=m2 a ...(ii) Add (i) and (ii) (3 g/2)((m1-m2/m1+m2))=a Use a in eq. (i) or (ii) Solving T=(3 m1 m2/m1+m2) g

Q. Two bodies of masses $m_{1}$ and $m_{2}$ are connected by a light string which passes over a frictionless, massless pulley. If the pulley is moving upward with uniform acceleration $\frac{g}{2}$ , then tension in the string will be

$\frac{3 m _{1} m _{2}}{m _{1} + m _{2}} g$

$\frac{m _{1} + m _{2}}{4 m _{1} m _{2}} g$

$\frac{2 m _{1} m _{2}}{m _{1} + m _{2}} g$

$\frac{m _{1} m _{2}}{m _{1} + m _{2}} g$

Writing equation from the reference frame of pulley
$\frac{3 m _{1} g}{2} - T = m_{1} a$ ...(i)
$T - \frac{3 m _{2} g}{2} = m_{2} a$ ...(ii)
Add (i) and (ii)
$\frac{3 g}{2} (\frac{m _{1} - m _{2}}{m _{1} + m _{2}}) = a$
Use a in eq. (i) or (ii)
Solving $T = \frac{3 m _{1} m _{2}}{m _{1} + m _{2}} g$

Q. Two bodies of masses m1​ and m2​ are connected by a light string which passes over a frictionless, massless pulley. If the pulley is moving upward with uniform acceleration 2g​, then tension in the string will be

m1​+m2​3m1​m2​​g

4m1​m2​m1​+m2​​g

m1​+m2​2m1​m2​​g

m1​+m2​m1​m2​​g

Writing equation from the reference frame of pulley 23m1​g​−T=m1​a ...(i) T−23m2​g​=m2​a ...(ii) Add (i) and (ii) 23g​(m1​+m2​m1​−m2​​)=a Use a in eq. (i) or (ii) Solving T=m1​+m2​3m1​m2​​g

Q. Two bodies of masses $m_{1}$ and $m_{2}$ are connected by a light string which passes over a frictionless, massless pulley. If the pulley is moving upward with uniform acceleration $\frac{g}{2}$ , then tension in the string will be

$\frac{3 m _{1} m _{2}}{m _{1} + m _{2}} g$

$\frac{m _{1} + m _{2}}{4 m _{1} m _{2}} g$

$\frac{2 m _{1} m _{2}}{m _{1} + m _{2}} g$

$\frac{m _{1} m _{2}}{m _{1} + m _{2}} g$