An object requires $500 \mathrm{~N}$ force to be pulled up on a $30^{\circ}$ frictionless smooth inclined…

An object requires $500 \mathrm{~N}$ force to be pulled up on a $30^{\circ}$ frictionless smooth inclined plane at a constant speed. The weight of the object is
  1. $500 \sqrt{2} \mathrm{~N}$
  2. $1000 \mathrm{~N}$
  3. $1000 \sqrt{2} \mathrm{~N}$
  4. $500 \sqrt{3} \mathrm{~N}$

Solution

For constant speed $\mathrm{F}=500 \mathrm{~N}$
$\begin{aligned} & \mathrm{mg} \sin 30^{\circ}=500 \mathrm{~N} \\ & \Rightarrow \mathrm{mg} \cdot \frac{1}{2}=500 \mathrm{~N} \\ & \Rightarrow \mathrm{mg}=1000 \mathrm{~N} \\ & \Rightarrow \text { weight }=1000 \mathrm{~N}\end{aligned}$

Asked in: AP EAMCET 2022 (08 Jul Shift 1)

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