Question

A particle of mass 2 kg is performing UCM has a velocity of 2 m/s and is traveling along a circle of radius 1 m. Then _____ N is its centripetal force a)2 b)4 c)6 d)8

Answer 1

Given :

❇ Mass of particle = 2kg

❇ Velocity of particle = 2m/s

❇ Radius of circular path = 1m

To Find :

✴ Centripetal force acting in the particle.

Concept :

⏭ Centripetal force is not a new kind of force. The material forces such as tension, gravitational force, electrical force, friction, etc., may act as the centripetal force in any circular motion.

⏭ Centripetal force is the name given to any force that provides radial inward acceleration to a body in circular motion.

⏭ For a body moving along a horizontal circular path, centripetal force is

$\bigstar\:\underline{\boxed{\bf{\red{F_c=\dfrac{mv^2}{r}}}}}$

• Fc denotes centripetal force
• m denotes mass of particle
• v denotes velocity of particle
• r denotes radius of circular path

Calculation :

$\dashrightarrow\sf\:F_c=\dfrac{mv^2}{r}\\ \\ \dashrightarrow\sf\:F_c=\dfrac{2\times (2)^2}{1}\\ \\ \dashrightarrow\sf\:F_c=2\times 4\\ \\ \dashrightarrow\underline{\boxed{\bf{\purple{F_c=8N}}}}\:\gray{\bigstar}$

Option-D ✔

Answer 2

Answer

$\bold{\bf{\blue{Centipetel\;Force\;,\;F_c=\frac{mv^2}{r} }}}$

where ,

• m = mass of the particle
• v = velocity of the particle
• r = radius of the circular path

Give ,

mass , m = 2 kg

velocity , v = 2 m/s

radius , r = 1 m

Now , sub. values in formula , we get ,

$\implies \bold{F_c=\frac{2*2^2}{1} }\\\\\implies \bold{F_c=8\;N}$

So , option (d) is correct.