SATHEE: Rotational Motion Question 80

Rotational Motion Question 80

Question: A solid cyclinder of mass 50 kg and radius 0.5 m is free to rotate about the horizontal axis. A massless string is wound round the cylinder with one end attached to it and other hanging freely. Tension in the string required to produce an angular acceleration of $2 r e v / s^{2}$ is

Options:

A) 25 N

B) 50 N

C) 78.5 N

D) 157 N

Show Answer

Answer:

Correct Answer: D

Solution:

$\Rightarrow$ $m = 50 k g \Rightarrow r = 0.5 \Rightarrow α = 2 r e v / s^{2}$

$\Rightarrow$ Torque produce by the tension in the string

$= T \times R = T \times 0.5 = \frac{T}{2} N m$ …(i)

We know $τ = / α$ ..(ii)

From Eqs.(i) and (ii),

$= (\frac{M R^{2}}{2}) \times (2 \times 2 π) \frac{r a d}{s^{2}}$

$∴$ $l_{solid cylinder} = \frac{M R^{2}}{2}$

$\frac{T}{2} = \frac{50 \times {(0.5)}^{2}}{2} \times 4 π$

$T = 50 \times \frac{1}{4} \times 4 π$

$= 50 π = 157 N$

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Rotational Motion Question 80

Question: A solid cyclinder of mass 50 kg and radius 0.5 m is free to rotate about the horizontal axis. A massless string is wound round the cylinder with one end attached to it and other hanging freely. Tension in the string required to produce an angular acceleration of 2rev/s2 is

Options:

Answer:

Solution:

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Question: A solid cyclinder of mass 50 kg and radius 0.5 m is free to rotate about the horizontal axis. A massless string is wound round the cylinder with one end attached to it and other hanging freely. Tension in the string required to produce an angular acceleration of $2 r e v / s^{2}$ is