Question

Two light strings of length\[4cm\]and\[3cm\] are tied to bob of weight\[500gm\]. The free ends of string are tied to pegs in the same horizontal line and separated by \[5cm\]. The ratio of tension in the longer string to that in shorter string is:
A. \[4:3\]
B. \[3:4\]
C. \[4:5\]
D. \[5:4\]

Answer 1

Hint We can solve this problem by looking at the bob given in the question that it will create a triangle with two string sand wall that is distance between the strings and by Pythagoras theorem we can say that the triangle is right angled triangle and easily we can find the ratio of tension forces between them.

Complete step by step answer In the given question we are given a bob having weight as, \[W = 500gm\]
And we are having two strings in which length of one of the strings is given as, \[{l_1} = 4cm\]
And length of other string is given as, \[{l_2} = 3cm\]
And through watching at the triangle we can say that it will create a right angle between the two strings given in the question, so to find the ratio between them as,
\[\cot (\theta ) = \dfrac{{{l_{short}}}}{{{l_{long}}}}\]
\[\cot (\theta ) = \dfrac{3}{4}\]

Therefore we get the answer as the B option.

Additional information In these types of questions we have to solve the problem by making the diagram of the figure and finding the type of triangle like in this question we are getting right angles triangle but in every question we would not be getting right angled so we have to take care of all trigonometric triangles.

Note In this question to solve the problem just take care of using the right trigonometric expression that we have used it through equating opposite forces on the bob that is the bob is at equilibrium and we can equate the horizontal forces and vertical forces. But we can not always make it; it depends on the equilibrium state of the bob.