A weight mg is suspended from the middle of a rope whose ends are at same level. If the rope is no longer horizontal, the minimum tension required to completely straighten the rope will be

Question

A weight mg is suspended from the middle of a rope whose ends are at same level. If the rope is no longer horizontal, the minimum tension required to completely straighten the rope will be (A)  mg  (B)  √mg  (C) Infinite (D) zero

Tardigrade Admin · Accepted Answer

The given situation can be shown as from figure 2T sin θ =mg or T=(mg/2 sin θ ) when rope is straight, θ =0o ∴ T=(mg/2 sin θ )=∞ (infinite)

Q. A weight $m g$ is suspended from the middle of a rope whose ends are at same level. If the rope is no longer horizontal, the minimum tension required to completely straighten the rope will be

$m g$

$m g$

Infinite

zero

The given situation can be shown as from figure
$2 T sin θ = m g$ or $T = \frac{m g}{2 s i n θ}$
when rope is straight,
$θ = 0^{o}$
$∴$ $T = \frac{m g}{2 s i n θ} = \infty$ (infinite)

Q. A weight mg is suspended from the middle of a rope whose ends are at same level. If the rope is no longer horizontal, the minimum tension required to completely straighten the rope will be

mg

mg​

Infinite

zero

The given situation can be shown as from figure 2Tsinθ=mg or T=2sinθmg​ when rope is straight, θ=0o ∴ T=2sinθmg​=∞ (infinite)

Q. A weight $m g$ is suspended from the middle of a rope whose ends are at same level. If the rope is no longer horizontal, the minimum tension required to completely straighten the rope will be

$m g$

$m g$

The given situation can be shown as from figure
$2 T sin θ = m g$ or $T = \frac{m g}{2 s i n θ}$
when rope is straight,
$θ = 0^{o}$
$∴$ $T = \frac{m g}{2 s i n θ} = \infty$ (infinite)