Question

In circular motion at a given instant centripetal acceleration is $3cm/s^2$ and the angle between the resultant acceleration and centripetal acceleration is ${45}^o$. At that instant the magnitude of the resultant acceleration is:

• A. $3cm/s^2$
• B. $4.2cm/s^2$
• C. $1.5cm/s^2$
• D. $2.8cm/s^2$

Answer 1

The correct option is B $4.2cm/s^2$

$\overrightarrow{a}$ is resultant acceleration

$\overrightarrow{a_c}$ is centripetal acceleration $=3\times {10}^{-2}m/s^2$

$\overrightarrow{a_t}$ is tangential acceleration

Since the between $\overrightarrow{a_c}$ and$\overrightarrow{a}$ is $45°$ then the angle between $\overrightarrow{a}$ and $\overrightarrow{a_t}$ is also $45°$ since angle between$\overrightarrow{a_c}$ and $\overrightarrow{a_t}$ is $90°$

$a\cos 45°=a_c\Rightarrow a=\frac{a_c}{\cos 45°}=3\times {10}^{-2}\times \sqrt{2}=4.2\times {10}^{-2}m/s^2=4.2cm/s^2$