System of Particles and Rotational Motion's Question 6 | Physics XI - Part 1 | NCERT Exemplar Questions

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MCQ (Single Correct Answer)

In problem 5, the CM of the plate is now in the following quadrant of x-y plane.

III

MCQ (Single Correct Answer)

The density of a non-uniform rod of length 1 m is given by $$\rho(x)=a\left(1+b x^2\right)$$ where, a and b are constants and $$0 \leq x \leq 1$$. The centre of mass of the rod will be at

$$\frac{3(2+b)}{4(3+b)}$$

$$\frac{4(2+b)}{3(3+b)}$$

$$\frac{3(3+b)}{4(2+b)}$$

$$\frac{4(3+b)}{3(2+b)}$$

MCQ (Single Correct Answer)

A merry-go-round, made of a ring-like platform of radius $$R$$ and mass $$M$$, is revolving with angular speed $$\omega$$. A person of mass $$M$$ is standing on it. At one instant, the person jumps off the round, radially away from the centre of the round (as seen from the round). The speed of the round of afterwards is

$$2 \omega$$

$$\omega$$

$$\frac{\omega}{2}$$

MCQ (Multiple Correct Answer)

Choose the correct alternatives

For a general rotational motion, angular momentum $$\mathbf{L}$$ and angular velocity $$\omega$$ need not be parallel.

For a rotational motion about a fixed axis, angular momentum $$\mathbf{L}$$ and angular velocity $$\omega$$ are always parallel.

For a general translational motion, momentum $$\mathbf{p}$$ and velocity $$\mathbf{v}$$ are always parallel.

For a general translational motion, acceleration $$\mathbf{a}$$ and velocity $$\mathbf{v}$$ are always parallel.

MCQ (Multiple Correct Answer)

Figure shows two identical particles 1 and 2, each of mass $$m$$, moving in opposite directions with same speed $$\mathbf{v}$$ along parallel lines. At a particular instant $$\mathbf{r}_1$$ and $$\mathbf{r}_2$$ are their respective position vectors drawn from point $$A$$ which is in the plane of the parallel lines. Choose the correct options.

Angular momentum $$I_1$$ of particle 1 about $$A$$ is $$I=m v\left(d_1\right)$$

Angular momentum $$I_2$$ of particle 2 about $$A$$ is $$I_2=\mathrm{mvr}_2$$

Total angular momentum of the system about $$A$$ is $$I=m v\left(\mathbf{r}_1+\mathbf{r}_2\right)$$

Total angular momentum of the system about $$A$$ is $$I=m v\left(d_2-d_1\right) \otimes$$

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