Question

A puck of mass $100\text{gm}$ is tied to a string and allowed to revolve in a horizontal circle of radius $2\text{cm}$ on a frictionless horizontal table as shown in the figure. Other end of the string passes through a small hole at the centre of the table and a load of mass $5\text{kg}$ is tied to the string. The suspended load remains in equilibrium while the puck revolves on the table. If the tension in the string is $x\left(\text{N}\right)$ and speed of the puck is $y\left(\text{cm/s}\right)$, then find the values of $x$ and $y$ respectively. Take $g=10{\text{m/s}}^2$.

• A. $50,316$
• B. $316,316$
• C. $50,795$
• D. $50,100$

Answer 1

The correct option is A $50,316$

Applying condition of equilibrium in vertical direction for mass ($m$) = $5\text{kg}$ from FBD gives:
$T-mg=0$
$\Rightarrow T=5\times 10=50\text{N}$


FBD for puck of $100\text{gm}$ mass:

Since, only a single string is used, tension $T$ will be same everywhere.

In the vertical direction, puck is in equilibrium. ($N=mg$)
Tension acts as the only source of centripetal force for $100\text{gm}$ puck
$\therefore T=\frac{m{v}^2}{r}$
$m=0.1\text{kg}\&r=2\text{cm}=0.02\text{m}$
$\Rightarrow v=\sqrt{\frac{Tr}{m}}=\sqrt{\frac{50\times 0.02}{0.1}}=3.16\text{m/s}=316\text{cm/s}$