Physics NCERT Exemplar Solutions Class 11th Chapter Seven

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

a, b, d

a) according to the perpendicular axes theorem statement 1 is wrong

b) As z'|z so distance between them = a $\frac{\sqrt[]{2}}{2}=\frac{a}{\sqrt[]{2}}$

So according to parallel axes theorem I_z'=I_z+m (a/ $\sqrt[]{2}$ )²= I_z+ma²/2

Hence b is true

c) z' is not parallel to z hence Parallel axes does not applied so statement is false

d) as x and y axes are symmetrical . hence I_x=I_y so d is true

d) as x and y axes are symmetrical . hence I_x=I_y so d is true

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

b, c

a) When r>r'

Torque about z-axis t=r $*$ F

b) t'=r' $*F$ which is along negative z axis

c) t_z=Fr = magnitude of torque about z axis where r is perpendicular between F and z axis so torque along positive z axis is greater than negative z axis.

d) We are always calculating resultant torque about common axis. Hence total torque not equal to combination of torque along both axis of z, because they are not on common axis.

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

a, b, c, d

As we know torque = r $*$ F = rFsin $\theta$

a) when forces act radially angle =0 hence torque =0

b) when forces are acting on the axis of rotation r=0 torque=0

c) when forces acting parallel to the axis of rotation angle =0 so torque =0

d) when torque by forces are equal and opposite torque net = t₁-t₂=0

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.