Question

a
3. A dot makes a turn in a circle 5 times in
second. The radius of the circle is 5 cm and
the dot moves uniformly, the acceleration
of the dot is (in SI units)
?
1)
2)212 3)zero 511
125
2.​

Answer 1

Given:

A dot makes a turn in a circle 5 times in

second. The radius of the circle is 5 cm and

the dot moves uniformly.

To find:

Acceleration of dot?

Calculation:

First, since the dot performs UNIFORM CIRCULAR MOTION, dot will only experience centripetal acceleration (and no tangential acceleration).

• Velocity of dot will be :

$\rm \: v = \dfrac{5 \times (2\pi r)}{t}$

$\rm \implies \: v = \dfrac{5 \times (2\pi \times \frac{5}{100} )}{1}$

$\rm \implies \: v = \dfrac{\pi}{2} \: m {s}^{ - 1}$

Now, acceleration :

$\rm \: a = \dfrac{ {v}^{2} }{r}$

$\rm \implies \: a = \dfrac{ {( \frac{\pi}{2}) }^{2} }{ \frac{5}{100} }$

$\rm \implies \: a = \dfrac{ {\pi}^{2} }{ 4 \times 0.05}$

$\rm \implies \: a = \dfrac{ {\pi}^{2} }{ 0.2}$

$\rm \implies \: a = 49.34 \: m {s}^{ - 2}$

So, acceleration is 49.34 m/s².

Answer 2

Explanation:

$Given:</p><p></p><p>A dot makes a turn in a circle 5 times in</p><p></p><p>second. The radius of the circle is 5 cm and</p><p></p><p>the dot moves uniformly.</p><p></p><p>To find:</p><p></p><p>Acceleration of dot?</p><p></p><p>Calculation:</p><p></p><p>First, since the dot performs UNIFORM CIRCULAR MOTION, dot will only experience centripetal acceleration (and no tangential acceleration).</p><p></p><p>Velocity of dot will be :</p><p></p><p>\rm \: v = \dfrac{5 \times (2\pi r)}{t}v=t5×(2πr)</p><p></p><p>\rm \implies \: v = \dfrac{5 \times (2\pi \times \frac{5}{100} )}{1}⟹v=15×(2π×1005)</p><p></p><p>\rm \implies \: v = \dfrac{\pi}{2} \: m {s}^{ - 1}⟹v=2πms−1</p><p></p><p>Now, acceleration :</p><p></p><p>\rm \: a = \dfrac{ {v}^{2} }{r}a=rv2</p><p></p><p>\rm \implies \: a = \dfrac{ {( \frac{\pi}{2}) }^{2} }{ \frac{5}{100} }⟹a=1005(2π)2</p><p></p><p>\rm \implies \: a = \dfrac{ {\pi}^{2} }{ 4 \times 0.05}⟹a=4×0.05π2</p><p></p><p>\rm \implies \: a = \dfrac{ {\pi}^{2} }{ 0.2}⟹a=0.2π2</p><p></p><p>\rm \implies \: a = 49.34 \: m {s}^{ - 2}⟹a=49.34ms−2</p><p></p><p>So, acceleration is 49.34 m/s².</p><p></p><p>$