Physics

Problem

Two small blocks P and Q of masses

m

and

2m

are attached to light, inextensible strings of lengths

r

and

\tfrac{1}{2}r

respectively. Each block is whirled in a horizontal circle on a smooth table, the planes of the two circles being the same. Block P moves with constant speed

v

while block Q moves with constant speed

3v

. a. (i) Derive expressions for the tensions

T_P

and

T_Q

in the strings of blocks P and Q in terms of

m

v

and

r

. b. (ii) Hence obtain the numerical ratio

T_P:T_Q

. c. (iii) The radius of the circular path of block P is now slowly reduced to

0.75\,r

while its speed

v

remains unchanged. By what factor does

T_P

change as a result of this adjustment?

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