Question 144: Work, Energy and Power & Circular Motion

Question

A conical pendulum of length 1 m makes an angle $$	heta $$ = 45
o
w.r.t. Z-axis and moves in a circle in the XY plane. The radius of the circle is 0.4 m and its center is vertically below O. The speed of the pendulum, in its circular path, will be: (Take g = 10 ms
−2
)

Accepted Answer

FBD of pendulum is :
$$	herefore\,\,\,$$  T sin $$	heta $$ = $${{m{v^2}} \over r}$$
T cos $$	heta $$ = mg
$$	herefore\,\,\,$$ tan $$	heta $$ = $${{{v^2}} \over {rg}}$$
$$ \Rightarrow $$$$\,\,\,$$ tan45
o
= $${{{v^2}} \over {rg}}$$
$$ \Rightarrow $$$$\,\,\,$$ v
2
= rg
$$ \Rightarrow $$$$\,\,\,$$ v = $$\sqrt {0.4 	imes 10} $$ = 2 m/s

Answer

0.4 m/s

Answer

4 m/s

Answer

0.2 m/s

Answer

2 m/s

Work, Energy and Power & Circular Motion

A conical pendulum of length 1 m makes an angle $\theta $ = 45 o w.r.t. Z-axis and moves in a circle in the XY plane. The radius of the circle is 0.4 m and its center is vertically below O. The speed of the pendulum, in its circular path, will be: (Take g = 10 ms −2 )

Choose the correct answer: