3since the pulley is acted upon by the tension it feels the torque.
and the string is not slipping so it is in pure rotation.
hey guys can ne1 help me wid this ? Its an hc verma prob n the answer is not coming right. the pulley has radius r and moment of inertia I n u r reqd 2 find the accn of da system. hcv says tht it is Mg/(m+M+I2/r). my question is: since the string dosnt slip over the pulley, then wy will accn depend on the pulley as well as the masses?
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6 Answers
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1think of two cases:
1) a smooth pulley not rotating abt its com ...
2) a smooth puly roating abt its com
in (1), the acc of teh blocks will not be affected by presence of pulley bcoz the pulley is not moving .
in (2), as the puley is also roating, it will add up some acceleration.
and how much is it ??
Fr=Ia/r [α=a/r as its pure rolling]
=> acceleration by this pulley = Fr2/I
1F for the above equation is T1-T2 difference in tension in the two strings.
so u have the three eqns :-
I) T1 - Mg = -Ma
II) T2 = ma
III) T1 - T2 = Ia/r2 [I and r are given.]
1but theres only 1 string...shouldnt the tension be same all throughout the string since it is massless?
1the tension in the string would have been same throughout had the pulley been irrotational and massless.
since the pulley isnt so,
therfore, tension in the two sections will be diff.
3hi aditya
see if we have same tension thruout the net torqe on the pulley will be zero and thus the system will remain in equilibrium ....!!!!!!!!!!!!!! butt this is not the case here ........ so the tensions are different ...............