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

Question

A solid sphere of density η(>1) times lighter than water is suspended in a water tank by a string tied to its base as shown in fig. If the mass of the sphere is m, then the tension -in the string is given by (A) ((η-1/η)) m g (B) η m g (C) (m g/η-1) (D) (η-1) m g

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/66b0c86991ae591bed77e0a055e3bbe4-.png" /> T+m g=Fb ∴ T =Fb-m g =Vρw g-m g =(m/(ρw / η)) ρw g-m g =(η-1) m g .

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

$(\frac{η - 1}{η}) m g$

$η m g$

$\frac{m g}{η - 1}$

$(η - 1) m g$

$T + m g = F_{b}$
$∴ T = F_{b} - m g$
$= V_{ρ_{w}} g - m g$
$= \frac{m}{( ρ _{w} / η )} ρ_{w} g - m g$
$= (η - 1) m g .$

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

(ηη−1​)mg

ηmg

η−1mg​

(η−1)mg