Mr. A, B and C are trying to put a heavy piston into a cylinder at a mechanical workshop in railway

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4-1.Newton's Laws of Motion

hard

Mr. $A, B$ and $C$ are trying to put a heavy piston into a cylinder at a mechanical workshop in railway yard. If they apply forces $F_1, F_2$ and $F_3$ respectively on ropes then for which set of forces at that instant, they will be able to perform the said job?

A$\sqrt{3} F_1=F_2+2 F_3$

B$2 F_1=F_2+F_3$

C$2 F_2=\sqrt{3} F_1-\frac{F_3}{2}$

D$F_3=2 F_1-\sqrt{3} F_2$

Solution

(a)
Piston is vertically above the cylinder so to drop it inside the cylinder, Net horizontal force must be zero on the piston
So,
$F_1 \sin 60=F_2 \cos 60+F_3$
$F_1 \frac{\sqrt{3}}{2}=\frac{F_2}{2}+F_3$
$\sqrt{3} F_1=F_2+2 F_3$

Standard 11

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hard

Mr. $A, B$ and $C$ are trying to put a heavy piston into a cylinder at a mechanical workshop in railway yard. If they apply forces $F_1, F_2$ and $F_3$ respectively on ropes then for which set of forces at that instant, they will be able to perform the said job?

Solution

Similar Questions

The boxes of masses $2\, {kg}$ and $8\, {kg}$ are connected by a massless string passing over smooth pulleys. Calculate the time taken by box of mass $8\; {kg}$ to strike the ground starting from rest. (use $\left.{g}=10\, {m} / {s}^{2}\right)$ (in ${s}$)

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