Two identical small balls A and B each of mass m connected by a light inextensible string of length l are placed on a frictionless horizontal floor. With what velocity u must the ball B be projected vertically upwards so that the ball A leaves the floor?

Question

Sanyam Shah · Answer

Apply the equation when system becomes vertical: T=mg (to lift it from the ground) T=mu 2 /l (centripetal force provided by tension to the other ball) Solve them and get answer u=root(gl)

Sanyam Shah · Answer

Above solution is wrong u = root(gl) is the final velocity of both the balls performing circular motion at that point to find initial speed u 0 apply energy cnservation law: 1/2m u 0 2 = 1/2mu 2 + mgl now keep the value of u in above equation and get answer u>=root(3gl)

Karl Marx · Answer

When Ball A leaves floor, N=0 So, T = mg ....(i) Also since Ball B undergoes circular motion wrt Ball A So, T = mv^2/l ....(ii) Now conserving Mechanical energy at ground and highest point, 1/2mu^2 = 1/2 mv^2 + mgl ….(iii) Solving all three equations we get, u = root(3gl) [And thats the final correct answer].

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Two identical small balls A and B each of mass m connected by a light inextensible string of length l are placed on a frictionless horizontal floor. With what velocity u must the ball B be projected vertically upwards so that the ball A leaves the floor?

Two identical small balls A and B each of mass m connected by a light inextensible string of length l are placed on a frictionless horizontal floor. With what velocity u must the ball B be projected vertically upwards so that the ball A leaves the floor?

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Two identical small balls A and B each of mass m connected by a light inextensible string of length l are placed on a frictionless horizontal floor. With what velocity u must the ball B be projected vertically upwards so that the ball A leaves the floor?

Two identical small balls A and B each of mass m connected by a light inextensible string of length l are placed on a frictionless horizontal floor. With what velocity u must the ball B be projected vertically upwards so that the ball A leaves the floor?

3 Answers

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