A carpet of mass M made of inextensible material is rolled along its length in the form of a cylinder of radius R and is kept on a rough floor. The carpet starts unrolling without sliding on the floor when a negligibly small push is given to it. If R = 1.05 m then calculate the horizontal velocity of the axis (in m/s) of the cylindrical part of the carpet when its radius reduces to R/2. (Take g = 10 m/s2)
Figure shows the forces acting on the carpet in two cases:
i. when the radius of the roll is R.
ii. when the radius is R/2
Mass of the roll of radius R/2 = M/4 (Mass is proportional to the area of cross section)
The mass of the part of the carpet spread on the floor = (3/4) M.
The mechanical energy of the system will remains constant.
The part of the carpet spread on the ground will have no kinetic energy.
According to conservation of energy,
…(i)
As the roll of the carpet is not sliding, we can consider that the roll of carpet as a rolling cylinder. We can calculate the kinetic energy of the moving cylindrical roll by the relation
M = mass of the roll at any time
Hence the kinetic energy of the roll when its radius is R/2
Change in kinetic energy,
Change in gravitational potential energy.
Finally substituting in the equation (i), we have
Talk to our academic expert!
Similar Questions
A homogeneous solid cylindrical roller of radius R and mass M is pulled on a cricket pitch by a horizontal force. Assuming rolling without slipping, angular acceleration of the cylinder is
799 666 8865
support@infinitylearn.com
6th Floor, NCC Building, Durgamma Cheruvu Road, Vittal Rao Nagar, HITEC City, Hyderabad, Telangana 500081.
JEE Mock Tests
JEE study guide
JEE Revision Notes
JEE Important Questions
JEE Sample Papers
JEE Previous Year's Papers
NEET previous year’s papers
NEET important questions
NEET sample papers
NEET revision notes
NEET study guide
NEET mock tests