A solid sphere of density α ( 1) times lighter than water is suspended in a water tank by a string tied to its base as shown in figure. If the mass of the sphere is m then the tension in the string is given by

Question

A solid sphere of density α (> 1) times lighter than water is suspended in a water tank by a string tied to its base as shown in figure. If the mass of the sphere is m then the tension in the string is given by <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-fqwreux47antwihr.jpg" /> (A) ((α - 1/α ))mg (B) α mg (C) (m g/α - 1) (D) (α - 1)mg

Tardigrade Admin · Accepted Answer

Density of sphere σ =(ρ ω /α ) <img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-fqwreux47antyqbi.jpg" /> (ρ ω /σ )=α FB=mg+T T=FB-mg=ρ ω Vg-mg =ρ ω (m/σ )g-mg =(((ρ )ω /σ ) - 1)mg=(α - 1)mg

Q. A solid sphere of density $α (> 1)$ times lighter than water is suspended in a water tank by a string tied to its base as shown in figure. If the mass of the sphere is $m$ then the tension in the string is given by

$(\frac{α - 1}{α}) m g$

$α m g$

$\frac{m g}{α - 1}$

$(α - 1) m g$

Density of sphere $σ = \frac{ρ _{ω}}{α}$

$\frac{ρ _{ω}}{σ} = α$
$F_{B} = m g + T$
$T = F_{B} - m g = ρ_{ω} V g - m g$
$= ρ_{ω} \frac{m}{σ} g - m g$
$= (\frac{( ρ ) _{ω}}{σ} - 1) m g = (α - 1) m g$

Q. A solid sphere of density α(>1) times lighter than water is suspended in a water tank by a string tied to its base as shown in figure. If the mass of the sphere is m then the tension in the string is given by

(αα−1​)mg

αmg

α−1mg​

(α−1)mg