Work, Energy and Power
|P.||(t) = αt + βt||1.|
|Q.||(t) = α cos ωt + β sin ωt||2.|
|R.||(t) = α (cos ωt + sin ωt)||3.||K|
This question has statement I and statement II. Of the four choices given after the statements, choose the one that best describes the two statements.
Statement − I: A point particle of mass m moving with speed ν collides with stationary point particle of mass M. if the maximum energy loss possible is given as .
Statement − II : Maximum energy loss occurs when the particles get stuck together as a result of the collision.
The work done on a particle of mass m by a force, (K being a constant of appropriate dimensions), when the particle is taken from the point (a, 0) to the point (0, a) along a circular path of radius a about the origin in the x-y plane is.
A bob of mass m, suspended by a string of length l1, is given a minimum velocity required to complete a full circle in the vertical plane. At the highest point, it collides elastically with another bob of mass m suspended by a string of length l2, which is initially at rest. Both the strings are mass-less and inextensible. If the second bob, after collision acquires the minimum speed required to complete a full circle in the vertical plane, the ratio is
A particle of mass 0.2 kg is moving in one dimension under a force that delivers a constant power 0.5 W to the particle. If the initial speed (in ms−1) of the particle is zero, the speed (in ms−1) after 5 s is
If the direct transmission method with a cable of resistance 0.4 Ω km−1 is used, the power dissipation (in %) during transmission is
A uniform force of Newton acts on a particle of mass 2 kg. Hence the particle is displaced from position meter to position meter. The work done by the force on the particle is :
A body of mass ‘m’ is taken from the earth’s surface to the height equal to twice the radius (R) of the earth. The change in potential energy of body will be:
Reason The total energy of an isolated system is conserved.
Reason Energy transfer in case of soft steel is large as in hard steel.
Two spheres A and B of masses m1and m2 respectively collide. A is at rest initially and B is moving with velocity v along x-axis. After collision B has a velocityin a direction perpendicular to the original direction.
The mass A moves after collision in the direction.
Reason: Momentum of earth + ball system remains constant.
A block of mass 0.18 kg is attached to a spring of force − constant 2 Nm-1. The coefficient of friction between the block and the floor is 0.1. Initially the block is at rest and the spring is un − stretched. An impulse is given to the block as shown in the figure. The block slides a distance of 0.06 m and comes to rest for the first time. The initial velocity of the block in ms-1 is V = N/10. Then N is
A block of mass 2 kg is free to move along the x-axis. It is at rest and from t = 0 onwards is is subjected to a time-dependent force F(t) in the x − direction. The force F (t) varies with t as shown in the figure. The kinetic energy of the block after 4.5 seconds is
Reason : Change in kinetic energy of particle is equal to the work done only in case of a system of one particle.
A point mass of 1kg collides elastically with a stationary point mass of 5kg. After their collision, the 1kg mass reverses its direction and moves with a speed of
2ms-1. Which of the following statement(s) is (are) correct for the system of these two masses.
Two small particles of equal masses start moving in opposite directions from a point A in a horizontal circuit orbit. Their tangential velocities are v and 2v respectively, as shown in the figure. Between collisions, the particles move with constant speeds. After making how many elastic collisions, other than that at A, these two particles will again reach the point A ?
Reason The potential energy of water at the top is converted into heat energy during falling.
Column II shows five systems in which two objects are labeled as X and Y, Also in each case a point P is shown. Column I give some statements about X and/or Y. Match these statements to the appropriate system(s) from column II.
|Column I||Column II|
|(A)||The force exerted by X on Y has a magnitude Mg||(p)||
Block Y of mass M left on a fixed inclined plane X, slides on it with a constant velocity
|(B)||The gravitational potential energy of X is continuously increasing||(q)||
Two ring magnets Y and Z each of mass M, are kept in frictionless vertical plastic stand so that they repeal each other. Y rests on the base X and Z hangs in air in equilibrium. P is the topmost point of the stand on the common axis of the two rings. The whole system is in a lift that is going up with a constant velocity
|(C)||Mechanical energy of the system X + Y is continuously decreasing||(r)||
A pulley Y of mass m0 is fixed to a table through a clamp X. A block of mass M hangs from a string that goes over the pulley and is fixed at point P of the table. The whole system is kept in a lift that is going down with a constant velocity
|(D)||The torque of the weight of Y about point P is zero||(s)||
A sphere Y of mass M is put in a nonviscous liquid X kept in a container at rest. The sphere is released and it moves down in the liquid
A sphere Y of mass M is falling with its terminal velocity in a viscous liquid X kept in a container
Three objects and are kept in a straight line on a frictionless horizontal surface. These have masses and respectively. The object moves towards with a speed and makes an elastic collision with it. Thereafter, makes completely inelastic collision with All motions occur on the same straight line. Find the final speed (in ms−1) of the object
If collision between the block and the incline is completely elastic, then the vertical (upward) component of the velocity of the block at point B, immediately after it strikes the second incline is
A block (B) is attached to two unstretched springs S1 and S2 with spring constants k and 4k, respectively (see figure I). The other ends are attached to identical supports M1 and M2 not attached to the walls. The springs and supports have negligible mass. There is no friction anywhere. The block B is displaced towards wall 1 by a small distance x (figure II) and released. The block returns and moves a maximum distance y towards wall 2. Displacement x and y are measured with respect to the equilibrium position of the block B. The ratio is
A bob of mass M is suspended by a massless string of length L. The horizontal velocity V at position A is just sufficient to make it reach the point B. The angle at which the speed of the bob is half of that at A, satisfies