Question

An L-shaped object, made of thin rods of uniform mass density, is suspended with a string as shown in figure. If AB = BC, and the angle made by AB with downward vertical is `theta`, then ____________.

Options

• `"tan"  theta  = 1/2`

• `"tan"  theta = 1/3`

• `"tan"  theta = 2/sqrt3`

• `"tan"  theta = 1/(2sqrt3)`

Answer 1

An L-shaped object, made of thin rods of uniform mass density, is suspended with a string as shown in figure. If AB = BC, and the angle made by AB with downward vertical is `theta`, then `"tan"  theta = 1/3`.

Explanation:

Assume m be the mass of one rod. At equilibrium,

`tau _(("rod" 1)) + tau _(("rod" 2)) = 0`

`"now, cos"  theta = "BD"/("L"//2)`

`therefore "BD" = "L"/2  "cos" theta`

`"sin"  theta = "BA"/"L"`

`therefore "BA" = "L sin"  theta`

`therefore "mg" ("L"/2  "sin" theta) - "mg" ("L"/2  "cos" theta - "L sin"  theta) = 0`

`therefore 3/2  "L sin" theta = "L"/2  "cos" theta Rightarrow "tan"  theta = 1/3`