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Rutherford's Set up and Predictions

The angular m...

Question

The angular momentum of the $α -$ particles which are scattered through large angles by the heavier nuclei, is conserved because

A

of the nature of repulsive forces

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B

the kinetic energy is conserved

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C

the potential energy is conserved

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D

there is no external torque

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Solution

The correct option is C there is no external torque
The angular momentum of $α$ particles is conserved because there is no external torque.

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Q. Kinetic energy of a system is always conserved, no matter what internal and external forces on the body are present

State if each of the following statements is true or false. Give reasons for your answer.

(a) In an elastic collision of two bodies, the momentum and energy of each body is conserved.

(b) Total energy of a system is always conserved, no matter what internal and external forces on the body are present.

(c) Work done in the motion of a body over a closed loop is zero for every force in nature.

(d) In an inelastic collision, the final kinetic energy is always less than the initial kinetic energy of the system.

Q. In the List-I below, four different paths of a particle are given as functions of time. In these functions,

α

β

are positive constants of appropriate dimensions and

α \neq B

. In each case, the force acting on the particle is either zero or conservative. In List-II, five physical quantities of the particle are mentioned;

\to p

is the linear momentum

\to L

is the angular momentum about the origin, K is the kinetic energy, U is the potential energy and E is the total energy. Match each path in List-I with those quantities in List-II, which are conserved for the path.

List - I	List - II
P. $\to r (t) = α t^i + β t^j$	1. $\to p$
Q. $\to r (t) = α c o s (ω t)^i + β s i n (ω t)^j$	2. $\to L$
R. $\to r (t) = α (c o s (ω t)^i + s i n (ω t)^j)$	3. K
S. $\to r (t) = α t^i + \frac{β}{2} t^{2}^j$	4. U
	5. E

Q. Three particles

α

-particle, proton and deuteron are accelerated by the same potential difference. What is the ratio of kinetic energy :

α

particle encounters a stationary unknown nucleus. After collision the two nuclei are scattered in mutually perpendicular directions. If some kinetic energy is lost in collision then unknown nucleus must be

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