Physics

Yes, the NCERT Exemplar is extremely important for entrance exam preparation. Those who are preparing for the NEET and JEE examinations must have a clear understanding of all the topics related to the chapter. The NCERT Exemplar contains advanced-level questions that are based on chapter 1 concepts and also similar questions those asked in the competitive exams. Practicing from Shiksha's NCERT Exemplar gives concept clarity, speed, and accuracy while solving the questions in CBSE or entrance exams.

The NCERT Exemplar provides a variety of higher-order thinking and application-based questions. It helps students deepen their understanding of Chapter Two Units and Measurements. The chapter helps students build a strong foundation for Physics advanced topics, prepares students for competitive exams, and improves their problem-solving skills.

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

(d) The bangle is in the form of ring. The centre of mass lies at the centre which is outside the body so C.O.M of bangle lies outside the circle.

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

Let b be the position vector of the centre of mass of a regular n-polygon.

(n-1) equal point masses are placed at (n-1) vertices of the regular n polygon, therefore for its centre of mass

r_CM= $\frac{\left(n-1\right)mb+ma}{\left(n-1\right)m+m}=0$

(n-1)mb+ma=0

B=- $\frac{a}{n-1}$

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

Where weight of the door acts along negative y axis

A force can produce torque only along a direction normal to itself as $\tau =r*F$ . So when the door is in the xy plane the torque produced by gravity can only along z direction. Never about an axis passing through y direction. Hence the weight will not produce any torque.

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.