Question

A particle of mass 1 kg is moving on a circular path of 10 m radius. At any instant of time, its speed is 5 $m{s}^{-1}$ and the speed is increasing at a rate of 2 $m{s}^{-2}$. The net force acting on the particle is

• A. $9.2N$
• B. $1.2N$
• C. $3.2N$
• D. $5.2N$

Answer 1

The correct option is C $3.2N$

Net acceleration is the resultant acceleration of centripetal acceleration and tangential acceleration thus find both of them as follows:

Let $a_c$ be the centripetal acceleration.

and $a_t$ be the tangential acceleration

At the given instant

Now then,

$a_c=\frac{v^2}{r}=\frac{5^2}{10}=2.5m/s^2$

$a_t=2m/s^2$

.

Net acceleration,

$a=\sqrt{a_c^2+a_t^2}$

$=\sqrt{{2.5}^2+2^2}=3.2m/s^2$

Net force on the particle,

$F=ma$

$⟹1\times 3.2=3.2N$