Class 11th

A proton is kept at rest. A positively charged particle is released from rest at a distance d in its field. Consider two experiments; one in which the charged particle is also a proton and in another, a positron. In the same time t, the work done on the two moving charged particles is

(a) Same as the same force law is involved in the two experiments.

(b) Less for the case of a positron, as the positron moves away more rapidly and the force on it weakens.

(c) More for the case of a positron, as the positron moves away a larger distance.

(d) Same as the work done by charged particle on the stationary proton.

An electron and a proton are moving under the influence of mutual forces. In calculating the change in the kinetic energy of the system during motion, one ignores the magnetic force of one on another. This is because,

(a) The two magnetic forces are equal and opposite, so they produce no net effect.

(b) The magnetic forces do no work on each particle.

(c) The magnetic forces do equal and opposite (but non-zero) work on each particle.

(d) The magnetic forces are necessarily negligible.

On complete combustion a litre of petrol gives off heat equivalent to 3*107 J. In a test drive a car weighing 1200 kg. including the mass of driver, runs 15 km per litre while moving with a uniform speed on a straight track. Assuming that friction offered by the road surface and air to be uniform, calculate the force of friction acting on the car during the test drive, if the efficiency of the car engine were 0.5.

An adult weighing 600N raises the centre of gravity of his body by 0.25 m while taking each step of 1 m length in jogging. If he jogs for 6 km, calculate the energy utilised by him in jogging assuming that there is no energy loss due to friction of ground and air. Assuming that the body of the adult is capable of converting 10% of energy intake in the form of food, calculate the energy equivalents of food that would be required to compensate energy utilised for jogging.

An engine is attached to a wagon through a shock absorber of length 1.5m. The system with a total mass of 50,000 kg is moving with a speed of 36 km h-1 when the brakes are applied to bring it to rest. In the process of the system being brought to rest, the spring of the shock absorber gets compressed by 1.0 m. If 90% of energy of the wagon is lost due to friction, calculate the spring constant.

Suppose the average mass of raindrops is 3.0 * 10-5kg and their average terminal velocity 9 m s^-1. Calculate the energy transferred by rain to each square metre of the surface at a place which receives 100 cm of rain in a year.

Two pendulums with identical bobs and lengths are suspended from a common support such that in rest position the two bobs are in contact). One of the bobs is released after being displaced by 10o so that it collides elastically head-on with the other bob.

(a) Describe the motion of two bobs.

(b) Draw a graph showing variation in energy of either pendulum with time, for 0≤t≤2T, where T is the period of each pendulum.

A raindrop of mass 1.00 g falling from a height of 1 km hits the ground with a speed of 50 ms^-1. Calculate

(a) The loss of P.E. of the drop. 

(b) The gain in K.E. of the drop. 

(c) Is the gain in K.E. equal to loss of P.E.? If not why. Take g = 10 ms^-2

The bob A of a pendulum released from horizontal to the vertical hits another bob B of the same mass at rest on a table as shown in Fig. 6.13. If the length of the pendulum is 1m, calculate

(a) The height to which bob A will rise after collision.

(b) The speed with which bob B starts moving. Neglect the size of the bobs and assume the collision to be elastic.

Consider a one-dimensional motion of a particle with total energy E. There are four regions A, B, C and D in which the relation between potential energy V, kinetic energy (K) and total energy E is as given below:

Region A : V > E

Region B : V < E

Region C : K > E

Region D : V > K

State with reason in each case whether a particle can be found in the given region or not.