A piece of uniform string hangs vertically so that it's free end just touches the horizontal surface of a table - Physics - Laws Of Motion

Question

A piece of uniform string hangs vertically so that it's free end
just touches the horizontal surface of a table If the upper end of
the string is released during the falling of the string,show that
total force on the surface is three times the weight of that part
of the string lying on the surface

Rajesh K Nimat · Accepted Answer

Dear student
when string has fallen through distance yv=2gyAfter this, the length vdt of the string shall fall in infinitely small timedt
 If dp is the momentum in time dt, thendp=mvdt
v  m is mass/lengthF=dpdt=mv2=m×2gy=2my gtotal force on table=2my g+myg=3my gThis equals the weight of the length 3y of the stringRegards

A piece of uniform string hangs vertically so that it's free end just touches the horizontal surface of a table. If the upper end of the string is released during the falling of the string,show that total force on the surface is three times the weight of that part of the string lying on the surface