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The diagram below shows the circular face of a clock with radius 20 cm

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Bunuel
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The diagram below shows the circular face of a clock with radius 20 cm [#permalink] New post   25 Apr 2019, 02:15
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The diagram below shows the circular face of a clock with radius 20 cm and a circular disk with radius 10 cm externally tangent to the clock face at 12 o'clock. The disk has an arrow painted on it, initially pointing in the upward vertical direction. Let the disk roll clockwise around the clock face. At what point on the clock face will the disk be tangent when the arrow is next pointing in the upward vertical direction?

(A) 2 o'clock
(B) 3 o'clock
(C) 4 o'clock
(D) 6 o'clock
(E) 8 o'clock


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Re: The diagram below shows the circular face of a clock with radius 20 cm [#permalink] New post   27 Apr 2019, 05:00
Bunuel wrote:

The diagram below shows the circular face of a clock with radius 20 cm and a circular disk with radius 10 cm externally tangent to the clock face at 12 o'clock. The disk has an arrow painted on it, initially pointing in the upward vertical direction. Let the disk roll clockwise around the clock face. At what point on the clock face will the disk be tangent when the arrow is next pointing in the upward vertical direction?

(A) 2 o'clock
(B) 3 o'clock
(C) 4 o'clock
(D) 6 o'clock
(E) 8 o'clock


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e94497740358c73cbf056b7bd46be244a502e289.png


circumference of clock ; 400pi and of arrow ; 200 pi
so for every complete 2 rotations the arrow will point up wards .. IMO C
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Re: The diagram below shows the circular face of a clock with radius 20 cm [#permalink] New post   27 Apr 2019, 05:34
circumference of the disc= 2*pi*r=2*pi*10=20pi
circumference of the path which center of the disk going to travel=2*pi*(R+r)=2*pi*(20+10)=60pi
Whenever the disk covers the distance equal to its circumference, the direction of the arrow will be upward. Hence after the center of the disk travels 20pi which is 1/3rd of the total path, direction of the arrow will be upwards.

Point on the clock face will the disk be tangent when the arrow is next pointing in the upward vertical direction=
1/3*12= 4 o'clock
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Re: The diagram below shows the circular face of a clock with radius 20 cm [#permalink] New post   27 Apr 2019, 05:47
circumference of a circle = 2*pi*r (you use the wrong formula bro)
and when the disk rotates on the clock, circumference of the path traveled by disk is 2*pi*(r+R)
where r= radius of disk
R= radius of clock
mohitranjan05 wrote:
circumference of clock=2π(20)²=800π
Circumference of the disk=2π(10)²=200π

So, disk will take 4 revolution to cover the entire clock.

this gives us that each complete revolution of the disk will account for 90° of the clock.

So, IMO the disk should be same at 4 o'clock.
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Re: The diagram below shows the circular face of a clock with radius 20 cm [#permalink]
27 Apr 2019, 05:47
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