Answer to Question #217280 in Mechanics | Relativity for ulmighty super

Question

On a plane inclined at an angle α=30⁰ to the horizontal, a small object of mass m=100mg is released and it slides without friction (given that g=9.8m/s² .). Which of following statements is correct?

A. The acceleration of the movement of this object is equal 4.9m/s² .

B. The normal reaction R to the inclined plane is 8.48Nc

C. The acceleration of the movement of this object is equal to 4.9m/s² .

D. None of the above

Answer 1

Explanations & Calculations

• Since there is no friction on the plane, it is a freefall on the plane. So the acceleration on the plane is just the component of the gravitationl acceleration experienced in a verticle freefall.
• So

$\qquad\qquad \begin{aligned} \small a_{plane}&=\small g\sin \alpha\\ &=\small 9.8ms^{-2}\times\sin{30}\\ &=\small 4.9 \, ms^{-2} \end{aligned}$

• So the first response is correct.

• The normal reaction can be calculated just by the resolution of forces as the forces in a plane perpendicular to the given plane are balanced as no acceleration is present.
• Then,

$\qquad\qquad \begin{aligned} \small R-mg \cos\alpha&=\small 0\\ \small R&=\small mg\cos\alpha=(100\times10^{-6}kg)\times9.8ms^{-2}\times\cos30\\ &=\small 8.48\times10^{-4}N \end{aligned}$

• As the second response does not include any exponent term, it needs to be rejected.

• Note: You should know the resolution of forces to figure out the workings of these kinds of questions.
• Refer to the sketch to get the idea.
• Keeping all the units in IS standard eases the simplification process of the calculations & compatibility of the units.