Physics

This is a multiple choice type question as classified in NCERT Exemplar

(a), (c) For general rotational motion where axis of rotation is not symmetric . angular momentum L and angular velocity w need not be parallel. For general translational motion momentum p=mv hence p and v are always parallel.

This is a multiple choice type question as classified in NCERT Exemplar

(a) As no external torque acts on the system, angular momentum should be conserved hence Iw=constant

Where I is moment of inertia of the system and w is the angular velocity of the system.

So I₁w₁= I₂w₂

Where w₁ and w₂ are angular velocities before and after jumping.

Iw= $\frac{I}{2}{w}_2$

w₂=2w

This is a multiple choice type question as classified in NCERT Exemplar

(a) Density is given as ρ (x) = a (1+bx²)

Where a and b are constant and 0 $\le x\le 1$

Let b=0 ρ (x) = a= constant

Hence COM will be at x =0.5m

Putting b=0 ain above option only a gives this answer.

We should not check options by putting a=0 because $\rho =0$  for a=0

This is a multiple choice type question as classified in NCERT Exemplar

(c) First the centre of mass of the system was on the dotted line and was shifted towards Q from the centre. When mass is removed it will be on the same line but shifed away from the centre and below 3^rd quadrant.

This is a multiple choice type question as classified in NCERT Exemplar

(b) When the small piece Q is removed and glued to the centre of the plate . the mass closer to the z axis . hence moment of inertia decreases.

This is a multiple choice type question as classified in NCERT Exemplar

(d) we know that angular acceleration $\alpha =\frac{dw}{dt}$ , given w=constant

where w is the angular velocity of the disc

$\alpha =\frac{dw}{dt}=\frac{0}{dt}=0$

Hence angular acceleration is zero.

This is a multiple choice type question as classified in NCERT Exemplar

(b) The initial velocity is v_i = ve_y and after reflecting from the wall the final velocity is v_f= -ve_y. The trajectory is described as r= ye_y+ae_z.

hence the change in momentum is r $*m\left(v_f-v_i\right)=2mva{e}_x$  .

This is a multiple choice type question as classified in NCERT Exemplar

(c) Centre of mass lies towards the part of system of higher mass. In the above diagram the lower part is heavier bigger mass is downward . So COM lies below diameter.

The NCERT Exemplar provides great study material for preparing for the exam. It can help immensely in scoring high in the class 11 Physics exam. It helps in strengthening the concepts and improving understanding of how to solve complex problems. However, it is advised that it should be practiced alongside the NCERT textbook. The students can first read the theory from the NCERT book and then study from the NCERT Exemplar to apply the theory in solving questions. The Exemplar is a great tool for practice and revision.