IIT JEE , AIEEE Forum - Physics , Mechanics - a uniform solid cylinder of radius r=15 cm rolls over a horizontal plane passing into an i

rautela

a uniform solid cylinder of radius r=15 cm rolls over a horizontal plane passing into an inclined plane forming an angle (alpha) = 30degree with the horizontal . find the max value of the velocity v which permits the cylinder to roll onto the inclined plane section without a jump.the sliding is assumed to be absent.

eistien

ok whats your question ???whats that i???

rautela

answer is 1m/s

eistien

oh i didnt ask for the answer but it is under pure rolling ah???

anchitsaini

considering pure rotational motion about instantaneous axis of rotation --

initially energy = mgR + 1/2 * I * w²

                     = mgR + 1/2 [ mR²/2 + mR²] (v / R)²

                     = mgR + 1/2 [ 3mR²/2 ] (v / R)²

final energy = mgh + 1/2 [ 3mR²/2 ] (v₁ / R)²

h = R cos @

hence

conserving energy we get --

3mv² / 4 + mgR = 3mv₁² / 4 + mgR cos @      ---------1

also as N = 0

mg cos @ provides necessary centripetal acceleration

we get

mg cos @ = mv₁² / R

v₁² = gR cos @

putting this value in 1

we get

v =

[gR(7 cos @ - 4)] / 3 = 1m/s on putting values

anchitsaini

Re:a uniform solid cylinder of radius r=15 cm rolls over a horizontal plane passing into a

shailesh_45

anchit how N=0

anchitsaini

for the cylinder to roll onto the inclined plane section without a JUMP, normal reaction has to be zero to get the maximum velocity .

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