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A ring of mass m can slide over a smooth vertical rod. The ring is connected to a spring of force constant k = 4mg/R where 2R is the natural length of the spring. The other end of the spring is fixed to the ground at a horizontal distance 2R from the base of the rod. The mass is released at a height of 1.5R from the ground.
The correct answer is: the velocity of the ring when it reaches the ground will be
A body is dropped from a certain height. When it loses U amount of its energy it acquires a velocity v. The mass of the body is :
The correct answer is:
A body is moved along a straight line by a machine delivering a constant power. The distance moved by the body in time t is proportional to :
The correct answer is: t^{3/2}
A self propelled vehicle of mass m whose engine delivers constant power P has an acceleration a = P/mv (assume that there is no friction). In order to increase its velocity from v_{1} to v_{2} the distance it has to travel will be :
The correct answer is:
A block attached to a spring, pulled by a constant horizontal force, is kept on a smooth surface as shown in the figure. Initially, the spring is in the natural state. Then the maximum positive work that the applied force F can do is :
[Given that spring does not break]
Applying workenergy theorem on the block, we get
Fl − kt^{2}/2 = 0
l = 2F/k
or work done = Fl = 2F^{2}/k
A block of mass m is attached to two unstretched springs of spring constants k_{1} and k_{2} as shown in figure. The block is displaced towards right through a distance x and is released. Find the speed of the block as passes through the means position shown.
The correct answer is:
The block of mass m initially at x = 0 is acted upon by a horizontal force at any position x is given as F = a – bx^{2}, where a > μmg, as shown in the figure. The coefficient of friction between the surfaces of contact is μ. The net work done on the blocks is zero. If the block travels a distance?
The correct answer is:
A man places a chain (of mass m and length l) on a table slowly. Initially the lower end of the chain just touches the table. The man drops the chain. When half of the chain is in vertical position. The work done by the man in this process is :
The work done by man is negative of magnitude of decrease in potential energy of chain
The correct answer is:
A body is projected with kinetic energy k at angle with the vertical. Neglecting friction, its potential energy at the highest point will be :
KE + PE = k
The correct answer is:
In the Figure, the ball A is released from rest when the spring is at its natural length. For the block B of mass M to leave contact with the ground of some stage, the minimum mass of A must be :
Let m be minimum mass of ball
Let mass A moves downwards by x.
From conservation of energy
For mass M to leave contact with ground,
The correct answer is: M/2
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