Physics

This is a short answer type question as classified in NCERT Exemplar

Wheel is a rigid body. The particles that constitute the wheel do experience a centripetal acceleration directed towards the centre. This acceleration arises due to internal elastic forces which cancel out in pairs.

In a half wheel the distribution of mass about its centre of mass is not symmetrical, therefore the direction of angular momentum of the wheel does not coincide with the direction of its angular velocity. Hence an external torque is required to maintain the motion of the wheel.

This is a short answer type question as classified in NCERT Exemplar

no $\sum _i{F}_i\ne 0$

The sum of torques about a certain point O $\sum _i{r}_i*F_i=0$

The sum of torques about any other O $\sum _i{r}_i{F}_i=0$

The sum of torques about any other point O'

$\sum _i(r_i-a)*F_i=\sum _i{r}_i*F_i-a*\sum _i{F}_i$

Here the second term need not vanish.

Sum of all torques about any point is zero.

This is a short answer type question as classified in NCERT Exemplar

Moment of force $\tau$ ₁= F (a)….anticlockwise

Moment of weight mg $\tau$ ₂=mg (a/2)……. (clockwise)

Cube will not exhibit motion then $\tau$ _{1 $=\tau$ 2}

$F*a=mg*\frac{a}{2}$

F=mg/2

Cube will rotate when $\tau$ _{1 $>\tau$ 2}

$F*a>mg*\frac{a}{2}$

F>mg/2

At a/3 from point A then

mg $*\frac{a}{3}=F*aorF=\frac{mg}{3}$

when F=mg/4 which is less then mg/3 there will be no motion.

This is a short answer type question as classified in NCERT Exemplar

As the slope of graph is positive and positive slope indicates anti clockwise rotation which is traditionally taken as positive.

This is a short answer type question as classified in NCERT Exemplar

The moment of inertia of the object I = $\sum m$ r² [sum of moment of inertia of each constituents particles]

All the mass in a cylinder lies at a distance R from the axis of symmetry but most of the mass of a solid sphere lies at a smaller distance than R.

This is a short answer type question as classified in NCERT Exemplar

When the vertical height of the objects is very small as compared to the earth's radius we call the objects small, otherwise it is extended. Building and ponds are small objects and deep lake and ocean are examples of extended objects.

This is a long answer type question as classified in NCERT Exemplar

Frictional force f is acting in the opposite direction of F . let the acceleration of centre of mass of disc be a then

F-f=Ma where M is the mass of the disc

$\alpha =\frac{a}{R}$

$\tau =I\alpha$

fR= (1/2 MR²) $\alpha$

so fR= (1/2MR²) (a/R)

Ma=2f

From the above equation

F = F/3

F< $\mu N$ = $\mu Mg$

f/3 < $\mu Mg$

F=3 $\mu Mg$

This is a long answer type question as classified in NCERT Exemplar

area of square = area of rectangular plate

C²=a $*$ b

(a) $\frac{I_{xR}}{I_{xS}}=\frac{b^2}{c^2}$ here bxRxS

(b) $\frac{I_{yR}}{I_{yS}}=\frac{a^2}{c^2}$ here a>c so I_yR>I_yS

(c) I_zR-I_{zS $\propto \left(a^2+b^2-2c^2\right)=a^2+b^2$} +2ab= (a-b)²

(I_zR-I_zS)>0

$\frac{I_{zR}}{I_{zS}}1$

This is a long answer type question as classified in NCERT Exemplar

(a) Situation as given below

(b) F' =F=F'' where F' and F'' are external forces through support.

So F_net=O

External torque = F $*3R$ (anticlockwise)

(c) Let w₁ and w₂ be the final angular velocities of smaller and bigger drum in both clockwise and anticlockwise . finally there will be no friction

hence Rw₁=2Rw₂

so $\frac{w_1}{w_2}=2$