Question

An object of mass 100 g move around circumference of circle of radius 2 m with constant angular spee
7.5 rad/s. Compute
a) linear speed​

Answer 1

Question :-

An object of mass 100 g move around circumference of circle of radius 2 m with constant angular speed 7.5 rad/s.

Answer:-

→ Linear speed (v) = 15 m/s

→ Centripetal force (f) = 11.25 N

To find :-

a) linear speed

Step - by - step explanation :-

Given that,

• Mass of object (m) = 100 g
• Radius of circle (r) = 2 m
• Angular speed = 7.5 rad/s
• Linear speed = ?

Solution :-

Let linear speed is "v" ,

We know that,

$\implies \: \boxed{\bf{ v \: = \: r \: \omega}} \\ \\ \implies \: \bf{v \: = 2 \times 7.5 }\\ \\ \implies \: \boxed{\bf{ v \: = 15 \: } \frac{m}{s} }\\ \\ \red{\omega\: is\: the \:angular\: speed} .$

Therefore, The linear speed of object is 15 m/s .

To find centripetal force ,

Again let, centripetal force if "f",

We know that,

$\implies \: \boxed{\bf{ f \: = m \: r \: { \omega}^{2} }}$

Firstly change the mass of object into kg,

→ m = 100 g = 0.1 kg

$\implies \: \bf{f \: = 0.1 \times 2 \times {(7.5)}^{2} } \\ \\ \implies \: \bf{f \: = 0.2 \times 56.25} \\ \\ \implies \: \boxed{ \bf{ f \: = 11.25}} \: N$

Hence, centripetal force is 11.25 N .