A wire of mass 9.8 × 10−3  kg per metre passes over a frictionless pulley fixed on the top of an inclined frictionless plane which makes an angle of 300  with the horizontal. Masses M1  and M2  are tied at the two ends of the wire. The mass M1  rests on the plane and mass M2  hangs freely vertically downwards. The whole system is in equilibrium. Now a transverse wave propagates along the wire with a velocity of 100 ms−1.  Find the value of (M1+ M2)  in kg.

Resolving M1g  into rectangular components, we have M1g sin 300  acting along the plane downwards, and M1g cos 300  acting perpendicular to the plane downwards.                      Let T be the tension in the wire and R be the reaction of plane on the mass M1.  Since the system is in equilibrium, therefore,         T=M1gsin300 ----------- (i) and R=M1gcos300                ---------- (ii)          T = M2g                                       --------- (iii) From (i) and (iii), we haveT=M1gsin300=M2g         --------- (iv) Velocity of transverse wave , v=Tm ,Where m is the mass per unit length of the wire. ∴v2=T/m,  or  T=v2m=(100)2×(9.8×10−3)=98N                From          (iii) , M2= T/g = 98/9.8 = 10kg.From          (iv) , M1= 2M2= 2 x 10 = 20kg.                                   ∴M1+M2=30kg