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25 Apr 2019, 02:15
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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27% (02:11) correct
73%
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wrong
based on 26
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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
Attachment:
e94497740358c73cbf056b7bd46be244a502e289.png [ 19.53 KiB | Viewed 5330 times ]
Archit3110
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27 Apr 2019, 05:00
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Bunuel
circumference of clock ; 400pi and of arrow ; 200 pi
so for every complete 2 rotations the arrow will point up wards .. IMO C
27 Apr 2019, 05:34
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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
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
