Question

A solid cylinder of mass m2 radius Rand a block of mass mi are connected by a light string passing over a smooth pulley as shown. Find minimum u for which the glinder will roll on the rough surface ? [Given th
at m:= 1kg, m2=4kg, R= 1m]​

Answer 1

Explanation:

Let α

1

and α

2

be the angular accelerations of the cylinder and the disc respectively.

As the linear acceleration of the string is constant, so we get

2R×α

1

=R×α

2

orα

2

=2×α

1

Now doing torque balance on the disc we get,

(T

2

−T

1

)R=(

2

MR

2

)(2α)

or

T

2

−T

1

=Ma ...(1)

Also using the FBD of the mass M we have

Mg−T

1

=Ma ...(2)

and torque balance about the instantaneous center of rotation of the cylinder we have

T

2

(2R)=

2

M(2R)

2

(α)orT

2

=Ma ....(3)

Adding (1),(2) and (3)

a=

3

g

Answer 2

2

Explanation:

i don't explain about it sorry but answer is really right