Question

$\Large\mathbb\pink{HLO\:BRAINLLIAC}$

A stone tied to the end of a string 50 cm long is whirled in a horizontal circle with a constant speed. If the stone makes 10 revolutions in 20 s, what is the magnitude of acceleration of the stone.

✒ No Spam.​

Answer 1

$\Large\bf{\color{indigo}GiVeN,}$

• A stone is tied to one end of string.

• Length of the string is 50 cm.

• Stone with string is whirled in a horizontal circle with constant speed.

• The stone makes 10 revolutions in 20s.

$\Large\bf{\color{cyan}To\:FiNd,}$

• The magnitude of acceleration of the stone.

$\Large\bf{\color{red}CaLcUlAtIoN,}$

¤ See the attachment.

✒ Given that stone with string is whirled in a horizontal circle with constant speed.

✒ Means the centripetal acceleration which keeps constant speed in rotation.

$\bf\pink{And}$

✒ We know that centripetal acceleration acts along the radius & towards the center of the circle.

$\orange\bigstar\:\:\bf\purple{Centripetal\:acceleration\:(a_c)\:=\:{\omega}^2\:r\:}--(1)$

$\bf\blue{Where,}$

• $\bf{\red{\omega}}\:=\:Angular\:Speed\:$

• $\bf{\red{r}}\:=\:Radius\:of\:circle\:$

$\green\bigstar\:\:\bf\pink{Angular\:Velocity\:(\omega)\:=\:\dfrac{Angular\:Displacement}{Time\:period}\:}$

$\longmapsto\:\:\bf{Angular\:Velocity\:(\omega)\:=\:\dfrac{\Phi}{t}\:}$

$\longmapsto\:\:\bf{Angular\:Velocity\:(\omega)\:=\:\dfrac{10\times {2\pi}}{20}\:}$

$\longmapsto\:\:\bf{Angular\:Velocity\:(\omega)\:=\:\dfrac{20\pi}{20}\:}$

$\longmapsto\:\:\bf\green{Angular\:Velocity\:(\omega)\:=\:\pi\:rad/sec\:}$

$\bf\red{Now,}$

$:\implies\:\:\bf{Centripetal\:acceleration\:(a_c)\:=\:{\pi}^2\times {50}\:}$

$:\implies\:\:\bf{Centripetal\:acceleration\:(a_c)\:=\:50{\pi}^2\:}$

$:\implies\:\:\bf{Centripetal\:acceleration\:(a_c)\:=\:50\times{(3.14)}^2\:}$

$:\implies\:\:\bf{Centripetal\:acceleration\:(a_c)\:=\:50\times{9.8596}\:}$

$:\implies\:\:\bf{Centripetal\:acceleration\:(a_c)\:=\:493.4\:cm/sec^2}$

$:\implies\:\:\bf\blue{Centripetal\:acceleration\:(a_c)\:\approx\:493\:cm/sec^2}$

$\Large\bf\therefore$ The magnitude of acceleration of the stone is $\bf\orange{493\:cm/sec^2}$.

Answer 2

ANSWER ÷

Radius =r=50cm=0.5m

Radius =r=50cm=0.5mIn 20 sec revolution =10

Radius =r=50cm=0.5mIn 20 sec revolution =10In 1 sec revolution =10/20=1/2 Hz

Radius =r=50cm=0.5mIn 20 sec revolution =10In 1 sec revolution =10/20=1/2 HzN=1/2Hz

Radius =r=50cm=0.5mIn 20 sec revolution =10In 1 sec revolution =10/20=1/2 HzN=1/2HzNow,

Radius =r=50cm=0.5mIn 20 sec revolution =10In 1 sec revolution =10/20=1/2 HzN=1/2HzNow,Angular velocity =W=2πn=w=2×3.14×0.5

Radius =r=50cm=0.5mIn 20 sec revolution =10In 1 sec revolution =10/20=1/2 HzN=1/2HzNow,Angular velocity =W=2πn=w=2×3.14×0.5Radial Acceleration =w

Radius =r=50cm=0.5mIn 20 sec revolution =10In 1 sec revolution =10/20=1/2 HzN=1/2HzNow,Angular velocity =W=2πn=w=2×3.14×0.5Radial Acceleration =w 2

Radius =r=50cm=0.5mIn 20 sec revolution =10In 1 sec revolution =10/20=1/2 HzN=1/2HzNow,Angular velocity =W=2πn=w=2×3.14×0.5Radial Acceleration =w 2 r

Radius =r=50cm=0.5mIn 20 sec revolution =10In 1 sec revolution =10/20=1/2 HzN=1/2HzNow,Angular velocity =W=2πn=w=2×3.14×0.5Radial Acceleration =w 2 rRadial Acceleration =(3.14)

Radius =r=50cm=0.5mIn 20 sec revolution =10In 1 sec revolution =10/20=1/2 HzN=1/2HzNow,Angular velocity =W=2πn=w=2×3.14×0.5Radial Acceleration =w 2 rRadial Acceleration =(3.14) 2

Radius =r=50cm=0.5mIn 20 sec revolution =10In 1 sec revolution =10/20=1/2 HzN=1/2HzNow,Angular velocity =W=2πn=w=2×3.14×0.5Radial Acceleration =w 2 rRadial Acceleration =(3.14) 2 ×0.5m/s

Radius =r=50cm=0.5mIn 20 sec revolution =10In 1 sec revolution =10/20=1/2 HzN=1/2HzNow,Angular velocity =W=2πn=w=2×3.14×0.5Radial Acceleration =w 2 rRadial Acceleration =(3.14) 2 ×0.5m/s 2

Radius =r=50cm=0.5mIn 20 sec revolution =10In 1 sec revolution =10/20=1/2 HzN=1/2HzNow,Angular velocity =W=2πn=w=2×3.14×0.5Radial Acceleration =w 2 rRadial Acceleration =(3.14) 2 ×0.5m/s 2 =4.93m/s

Radius =r=50cm=0.5mIn 20 sec revolution =10In 1 sec revolution =10/20=1/2 HzN=1/2HzNow,Angular velocity =W=2πn=w=2×3.14×0.5Radial Acceleration =w 2 rRadial Acceleration =(3.14) 2 ×0.5m/s 2 =4.93m/s 2

Radius =r=50cm=0.5mIn 20 sec revolution =10In 1 sec revolution =10/20=1/2 HzN=1/2HzNow,Angular velocity =W=2πn=w=2×3.14×0.5Radial Acceleration =w 2 rRadial Acceleration =(3.14) 2 ×0.5m/s 2 =4.93m/s 2 =493cm/s

Radius =r=50cm=0.5mIn 20 sec revolution =10In 1 sec revolution =10/20=1/2 HzN=1/2HzNow,Angular velocity =W=2πn=w=2×3.14×0.5Radial Acceleration =w 2 rRadial Acceleration =(3.14) 2 ×0.5m/s 2 =4.93m/s 2 =493cm/s 2

I hope it helps u