A uniform sphere of weight W and radius 5, cm | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let the center of the sphere be $O$ and the point where the string is attached to the wall be $P$. Let the point of contact between the sphere and

Vedclass · Accepted Answer

$\frac{13}{12}\,W$

Vedclass · Answer

(D) Let the center of the sphere be $O$ and the point where the string is attached to the wall be $P$. Let the point of contact between the sphere and the wall be $Q$. The radius of the sphere is $r = 5\, cm$. The length of the string is $l = 8\, cm$. In the right-angled triangle formed by the center of the sphere $O$,the point of contact $Q$,and the attachment point $P$,the hypotenuse $OP = l + r = 8 + 5 = 13\, cm$. The base $OQ = r = 5\, cm$. Using the Pythagorean theorem,the vertical distance $PQ = \sqrt{OP^2 - OQ^2} = \sqrt{13^2 - 5^2} = \sqrt{169 - 25} = \sqrt{144} = 12\, cm$. Let $	heta$ be the angle the string makes with the vertical wall. Then $\cos 	heta = \frac{PQ}{OP} = \frac{12}{13}$. For the sphere to be in equilibrium,the vertical component of the tension $T$ must balance the weight $W$ of the sphere. Thus,$T \cos 	heta = W$. Substituting the value of $\cos 	heta$,we get $T 	imes \frac{12}{13} = W$,which implies $T = \frac{13}{12} W$.

$A$ uniform sphere of weight $W$ and radius $5\, cm$ is held by a string of length $8\, cm$ attached to a smooth vertical wall as shown in the figure. The tension in the string is:

Similar Questions

$A$ small child tries to move a large rubber toy placed on the ground. The toy does not move but gets deformed under her pushing force $F$,which is obliquely upward as shown in the figure. Then,

When is an object said to be in equilibrium?

Two masses $m$ and $M$ are attached to the strings as shown in the figure. If the system is in equilibrium,then

In the figure,the tension in the diagonal string is $60\,N$. Find the magnitude of the horizontal forces $\overline{F}_1$ and $\overline{F}_2$ that must be applied to hold the system in the position shown. What is the weight of the suspended block?

$A$ book of mass $5 \,kg$ is placed on a table and it is pressed by $10 \,N$ force. Then,the normal force exerted by the table on the book is ......... $N$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module