question_answer

An insect of mass m, starts moving on a rough inclined surface from point A. As the surface is very sticky, the coefficient of friction between the insect and the incline is\[\mu \text{ }=\text{ }1\]. Assume that it can move in any direction, up the incline or down the incline then

A) The maximum possible acceleration of the insect can be \[14\text{ }m/{{s}^{2}}\]

B) The maximum possible acceleration of the insect can be \[\text{2 }m/{{s}^{2}}\]

C) the insect can move with a constant velocity  

D) the insect cannot move with a constant velocity

Correct Answer: C

Solution :

[c] \[\operatorname{mg}\,sin\theta +mg cos \theta =ma\] \[a=g\,\sin \theta +g\cos \theta =10\left[ \frac{3}{5}+\frac{4}{5} \right]=14m/{{\sec }^{2}}\] \[\operatorname{If}\,{{f}_{r}}=mg\,\sin \theta \] \[=mg\times \frac{3}{5}=\frac{3mg}{5}<{{f}_{r\max }}\] \[{{f}_{r}}<{{f}_{r\max }}\] \[\frac{3mg}{5}<\frac{4mg}{5}\] Hence, insect can move with constant velocity.