A body is moving up an inclined plane of angle $\theta$ with an initial kinetic energy $E$. The coefficient…

1. $\frac{\mu \cos \theta}{E \cos \theta+\sin \theta}$
2. $E$
3. $\frac{\mu E \cos \theta}{\mu \cos \theta-\sin \theta}$
4. $\frac{\mu E \cos \theta}{\mu \cos \theta+\sin \theta}$ Increase in KE, $\begin{aligned} \frac{p_2^2-p_1^2}{2 m} & =\frac{(10)^2-(8)^2}{2 \times 4} \\ & =\frac{100-64}{8}=\frac{36}{8} \\ & =4.5 \mathrm{~J}\end{aligned}$

Solution

Acceleration of a body up a rough inclined plane
$a=g(\mu \cos \theta+\sin \theta)$ From equation of motion $\begin{aligned} v^2 & =u^2-2 a s \\ 0 & =u^2-2 a s \\ u^2 & =2 a s \end{aligned}$ Initial $\mathrm{KE}, E=\frac{1}{2} m u^2$ $\begin{aligned} E & =\frac{1}{2} m(2 a s) \\ s & =\frac{E}{m a} \end{aligned}$ $\begin{aligned} & \text { Work done } W=F \cdot s \\ & =(m g \sin \theta+\mu R) \cdot \frac{E}{m a} \\ & =(m g \sin \theta+\mu m g \cos \theta) \cdot \frac{E}{m(\mu \cos \theta+\sin \theta)} \\ & =g(\sin \theta+\mu \cos \theta) \cdot \frac{E}{g(\mu \cos \theta+\sin \theta)}=E\end{aligned}$

Asked in: AP EAMCET 2002

Practice more Work Power Energy questions on Aicharya