A uniform sphere of weight w and radius 3 m is being held by a string of length 2 m and attached to a frictionless wall, as shown in the figure. The tension in the string will be

Question

A uniform sphere of weight w and radius 3 m is being held by a string of length 2 m and attached to a frictionless wall, as shown in the figure. The tension in the string will be <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-e3kbsxkmsaemenj7.jpg" /> (A) (5 w/4) (B) (15 w/4) (C) (15 w/6) (D) none of these

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-e3kbsxkmsaemkmul.jpg" /> From geometry: cos θ =(3/5) sin θ =(4/5) As the sphere is at equilibrium Tsin θ =w T=(5 w/4)

Q. A uniform sphere of weight $w$ and radius $3 m$ is being held by a string of length $2 m$ and attached to a frictionless wall, as shown in the figure. The tension in the string will be

$\frac{5 w}{4}$

$\frac{15 w}{4}$

$\frac{15 w}{6}$

none of these

From geometry:
$cos θ = \frac{3}{5}$
$s in θ = \frac{4}{5}$
As the sphere is at equilibrium
$T s in θ = w$
$T = \frac{5 w}{4}$

Q. A uniform sphere of weight w and radius 3m is being held by a string of length 2m and attached to a frictionless wall, as shown in the figure. The tension in the string will be

45w​

415w​

615w​