Two weights w1 and w2 are suspended from the ends of a light string passing over a smooth fixed pulley. If the pulley is pulled up with acceleration g , the tension in the string will be

Question

Two weights w1 and w2 are suspended from the ends of a light string passing over a smooth fixed pulley. If the pulley is pulled up with acceleration g , the tension in the string will be (A) (4 w1 w2/w1 + w2) (B) (2 w1 w2/w1 + w2) (C) (w1 - w2/w1 + w2) (D) (w1 w2/2 (w1 - w2))

Tardigrade Admin · Accepted Answer

For solving the problem, we assume that observer is situated in the frame of pulley (non - inertial reference frame).
Solution

m_{1} g = w_{1}

m_{2} g = w_{2}

From force diagram [a],

T - m_{2} a_{0} - w_{2} = m_{2} a

Or

T - m_{2} g - w_{2} = m_{2} a

(∵ a_{0} = g)

Or

T - 2 w_{2} = m_{2} a

.....(i)
From force diagram [b],

m_{1} a_{0} + w_{1} - T = m_{1} a

Or

m_{1} g + w_{1} - T = m_{1} a

(∵ a_{0} = g)

Or

2 W_{1} - T = m_{1} a

......(ii)
From equations (i) and (ii),

T = \frac{4 w _{1} w _{2}}{w _{1} + w _{2}}

Q. Two weights $w_{1}$ and $w_{2}$ are suspended from the ends of a light string passing over a smooth fixed pulley. If the pulley is pulled up with acceleration $g$ , the tension in the string will be

$\frac{4 w _{1} w _{2}}{w _{1} + w _{2}}$

$\frac{2 w _{1} w _{2}}{w _{1} + w _{2}}$

$\frac{w _{1} - w _{2}}{w _{1} + w _{2}}$

$\frac{w _{1} w _{2}}{2 ( w _{1} - w _{2} )}$

Q. Two weights w1​ and w2​ are suspended from the ends of a light string passing over a smooth fixed pulley. If the pulley is pulled up with acceleration g , the tension in the string will be

w1​+w2​4w1​w2​​

w1​+w2​2w1​w2​​

w1​+w2​w1​−w2​​

2(w1​−w2​)w1​w2​​

Q. Two weights $w_{1}$ and $w_{2}$ are suspended from the ends of a light string passing over a smooth fixed pulley. If the pulley is pulled up with acceleration $g$ , the tension in the string will be

$\frac{4 w _{1} w _{2}}{w _{1} + w _{2}}$

$\frac{2 w _{1} w _{2}}{w _{1} + w _{2}}$

$\frac{w _{1} - w _{2}}{w _{1} + w _{2}}$

$\frac{w _{1} w _{2}}{2 ( w _{1} - w _{2} )}$