A particle experiences a variable force in a horizontal xy plane. Assume distance in meters and force in newton. If the particle moves from point (1, 2) to point (2, 3) in the xy plane; then kinetic energy changes by
A stone of mass m tied to a string is being whirled in a vertical circle with a uniform speed. The tension in the string is
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A block of mass 'm' (as shown in figure) moving with kinetic energy E compresses a spring through a distance 25 cm when its speed is halved. The value of spring constant of used spring will be nE Nm1 for n = _____________. (in integers)
Two cylindrical vessels of equal crosssectional area 16 cm^{2} contain water up to heights 100 cm and 150 cm, respectively. The vessels are interconnected so that the water levels in them become equal. The work done by the force of gravity during the process is: [Take density of water = 10^{3} kg/m^{3} and g = 10 ms^{2}]
A block of mass m attached to a massless spring is performing oscillatory motion of amplitude 'A' on a frictionless horizontal plane. If half of the mass of the block breaks off when it is passing through its equilibrium point, the amplitude of oscillation for the remaining system become fA. The value of f is
As per the given figure, two blocks each of mass 250 g are connected to a spring of spring constant 2 Nm1. If both are given velocity v in opposite directions, then maximum elongation of the spring is:
A body of mass 0.5 kg travels on a straight line path with velocity v = (3x^{2} + 4) m/s. The net work done by the force during its displacement from x = 0 to x = 2 m is:
A particle of mass 500 gm is moving in a straight line with velocity v = b x^{5/2}. The work done by the net force during its displacement from x = 0 to x = 4 m is: (Take b = 0.25 m^{3/2} s^{1})
A body of mass M at rest explodes into three pieces, in the ratio of masses 1 : 1 : 2. Two smaller pieces fly off perpendicular to each other with velocities of 30 ms1 and 40 ms1 respectively. The velocity of the third piece will be:
A free electron of 2.6 eV energy collides with a H^{+} ion. This results in the formation of a hydrogen atom in the first excited state and a photon is released. Find the frequency of the emitted photon (h = 6.6 × 10^{34} J s).
A particle of mass 1 kg is hanging from a spring of force constant 100 Nm^{1}. The mass is pulled slightly downward and released, so that it executes free simple harmonic motion with time period T. The time when the kinetic energy and potential energy of the system will become equal is The value of x is _______. (in integers)
Given below is the plot of a potential energy function U(x) for a system, in which a particle is in one dimensional motion, while a conservative force F(x) acts on it. Suppose that Emech = 8 J, the incorrect statement for this system is:
A body at rest is moved along a horizontal straight line by a machine delivering a constant power. The distance moved by the body in time 't' is proportional to
In a spring gun having spring constant 100 N/m, a small ball 'B' of mass 100 g is put in its barrel (as shown in figure) by compressing the spring through 0.05 m. There should be a box placed at a distance 'd' on the ground so that the ball falls in it. If the ball leaves the gun horizontally at a height of 2 m above the ground, the value of d is _______________ m.
(g = 10 m/s^{2}) (in integers)
A 60 HP electric motor lifts an elevator having a maximum total load capacity of 2000 kg. If the frictional force on the elevator is 4000 N, the speed of the elevator at full load is close to: (1 HP = 746 W, g = 10 ms^{2})
Physically, the notion of potential energy is applicable only to
A bolt of mass 0.3 kg falls from the ceiling of an elevator moving down with an uniform speed of 7 m/s. It hits the floor of the elevator (length of the elevator = 3 m) and does not rebound. What is the heat produced by the impact?
In which of the following cases is the work done positive?
The total mechanical energy of a system is conserved if the
The casing of a rocket in flight burns up due to friction. At whose expense is the heat energy required for burning obtained?
A tandem (twoperson) bicycle team must overcome a force of 165 N to maintain a speed of 9.00 m/s. Find the power required per rider, assuming that each contributes equally.
For a ball dropped from a tower of height h the total mechanical energy is
A trolley of mass 200 kg moves with a uniform speed of 36 km/h on a frictionless track. A child of mass 20 kg runs on the trolley from one end to the other (10 m away) with a speed of 4 ms^{−1} relative to the trolley in a direction opposite to the its motion, and jumps out of the trolley. How much has the trolley moved from the time the child begins to run?
A 50.0kg marathon runner runs up the stairs to the top of a 443mtall Tower. To lift herself to the top in 15.0 minutes, what must be her average power output?
In which of the following cases is the work done positive?
The launching mechanism of a toy gun consists of a spring of unknown spring constant. When the spring is compressed 0.120 m, the gun, when fired vertically, is able to launch a 35.0g projectile to a maximum height of 20.0 m above the position of the projectile before firing. Neglecting all resistive forces, determine the spring constant.
If F is a force and d is the displacement in the direction of force then the work done by the force is given by
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