Question

A car of mass $1000kg$ moving on a circular track of radius $100m$ with increase in speed at a rate of $8m/s^2$, if at an instant its speed is $30m/s$ then the acceleration of the car is (at this instant only)

• A. $>12$
• B. $<12$
• C. $=12$
• D. $Noneofthese$

Answer 1

The correct option is C $=12$

Given that,

Mass $m=1000kg$

Radius $r=100m$

Speed $v=30m/s$

Tangential acceleration $a_t=8m/s$

Now,

Radial acceleration is

$a_r=\frac{v^2}{r}$

$a_r=\frac{30\times 30}{100}$

$a_r=9m/s$

The resultant acceleration is

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

$a=\sqrt{8^2+9^2}$

$a=\sqrt{64+81}$

$a=12.04$

$a=12m/s^2$

Hence, the acceleration is $12m/s^2$