Question

A body of weight 200N moves in a horizontal circular path of radius 10m with speed of 10ms^-1. What is the centripetal force acting on the body? (g=10ms^-2).

Answer 1

$\huge{\bold{\underline{\underline{....Answer....}}}}$

$\huge{\bold{\underline{Given:-}}}$

• Weight of body (W) = 200N.
• Radius of circular path (r) = 10 m.
• Speed of the body (v) = 10 m/s.
• Acceleration due to gravity (g) = 10 m/s².

$\huge{\bold{\underline{Explanation:-}}}$

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Firstly Finding The Mass of the body.

Therefore,

$\large{\boxed{\tt W = mg}}$

Substituting the values,

$\large{\tt \implies 200 = m \times 10}$

$\large{\tt \implies m = \dfrac{200}{10}}$

$\large{\tt \implies m = \dfrac{20\cancel{0}}{\cancel{10}}}$

It becomes,

$\large{\boxed{\tt m = 20 \: Kg}}$

So, the mass of the body is 20Kg.

$\rule{300}{1.5}$

$\rule{300}{1.5}$

Now, From Expression Of Centripetal Force.

$\large{\boxed{\tt F = \dfrac{mv^2}{r}}}$

Substituting the values,

$\large{\tt \implies F = \dfrac{20 \times (10)^2}{10}}$

$\large{\tt \implies F = \dfrac{20 \times 100}{10}}$

$\large{\tt \implies F = \dfrac{2\cancel{0} \times 100}{\cancel{10}}}$

$\large{\tt \implies F = 2 \times 100}$

$\huge{\boxed{\boxed{\tt F = 200 \: N}}}$

So, The Centripetal Force acting on the body is 200N.

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Some Important formulas:-

• Tangential acceleration = ${\tt \dfrac{dv}{dt}}$

• Centripetal acceleration = ${\tt \dfrac{v^2}{r}}$

• Relation b/w Angular velocity and Linear velocity v = rω.

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Answer 2

$\huge{\star}{\underline{\boxed{\red{\sf{Answer :}}}}}{\star}$

Given :-

Weight of body (W) = 200 N

Radius of path = 10 m

Speed (v) = 10 m/s

Take g as 10 m/s²

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To Find :-

Centripetal force acting on body

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Solution :-

As, we know that

$\Huge{\boxed{\boxed{\green{\sf{Mass \: = \: \frac{Weight}{g}}}}}}$

____________[Put Values]

$\Large \rightarrow {\sf{Mass \: = \: \frac{20 \cancel{0}}{\cancel{10}}}}$

$\LARGE \implies {\boxed{\boxed{\sf{Mass \: = \: 20 \: kg}}}}$

$\rule{200}{3}$

For Calculating value of Centripital force we have formula :-

$\Huge{\boxed{\boxed{\orange{\sf{F_{c} \: = \: \frac{mv^2}{r}}}}}}$

Where,

Fc is centripital force

r is radius

m is mass

v is velocity

____________[Put Values]

$\Large \rightarrow {\sf{F_{c} \: = \: \frac{20 \: \times \: (10)^2}{10}}}$

$\Large \rightarrow {\sf{F_{c} \: = \: \frac{20 \: \times \: 10 \cancel{0}}{\cancel{10}}}}$

$\Large \rightarrow {\sf{F_{c} \: = \: 20 \: \times \: 10}}$

$\Huge \implies {\boxed{\boxed{\sf{F_{c} \: = \: 200 \: N}}}}$

∴ Centripital force is 200 N