# A driving pulley of 50 cm diameter running at 1000 rpm is connected to a driven pulley by belt.The driven pulley runs at 5000 rpm .find da diameter of da driven consider the slip in da belt as 5%. The option are 8.5 cm 9.0 cm 9.5 cm 10 cm

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by Monty1992

2014-10-04T21:06:56+05:30

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driving pulley:                          driven pulley:
Diameter = 50cm                    Diameter = dcm
rotation = 1000rpm                  rotation = 5000rpm

Slip in belt = 5%
efficiency = 100-5 = 95% = 0.95

0.95(1000×π×50) = 5000×π×d

⇒ d =

⇒  d = 9.5cm
Thanx for help
Which formula have u used it??
Think of the pulley as a wheel and the distance travelled when rotates at 1000rpm
2014-10-06T18:29:48+05:30

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When a bicycle travels on the road, each wheel turns n rotations per minute.  In one rotation the front wheel moves 2 π * radius on the road.   The front wheel moves  2π * radius * n  distance on the road.  As the distance traveled by both wheels is the same. Both the wheels have same radius.  The rpm of both wheels will also be same.
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Usually, the distance traveled by a point on the cylindrical surface of each pulley is same.  The belt strapped on both pulleys also rotates with same linear velocity all along the belt. But the radius and angular velocity will be different for both pulleys.

Linear velocity of belt = angular velocity of driving pulley * its radius
= angular velocity of driven pulley * its radius
v = ω1 * r1 = ω2 * r2

But there is a slip in the belt because  it is not very tightly strapped on the pulleys. It means that the angular velocity of the driven pulley will be 95% of the driving pulley. It also means that the linear velocity of a point on the cylindrical surface of driven pulley is only 95% of that of driving pulley.

So,     (1000 * 2 π ) * (50/2)  95% = (5000 * 2 π)  * r2

r2 = 5 * 0.95 = 4.75 cm

Diameter is = 2 r2 = 9.5 cm