A circular ring and a solid sphere having same radius roll down on an inclined plane from rest without slipping. The ratio of their velocities when reached at the bottom of the plane is $\sqrt{\frac{\mathrm{x}}{5}}$ where $\mathrm{x}=$ _______.
If $\overrightarrow{\mathrm{L}}$ and $\overrightarrow{\mathrm{P}}$ represent the angular momentum and linear momentum respectively of a particle of mass ' $m$ ' having position vector $\overrightarrow{\mathrm{r}}=\mathrm{a}(\hat{\mathrm{i}} \cos \omega \mathrm{t}+\hat{\mathrm{j}} \sin \omega \mathrm{t})$. The direction of force is
Which of the following are correct expression for torque acting on a body?
A. $\ddot{\tau}=\ddot{\mathrm{r}} \times \ddot{\mathrm{L}}$
B. $\ddot{\tau}=\frac{\mathrm{d}}{\mathrm{dt}}(\ddot{\mathrm{r}} \times \ddot{\mathrm{p}})$
C. $\ddot{\tau}=\ddot{\mathrm{r}} \times \frac{\mathrm{d} \dot{\mathrm{p}}}{\mathrm{dt}}$
D. $\ddot{\tau}=\mathrm{I} \dot{\alpha}$
E. $\ddot{\tau}=\ddot{\mathrm{r}} \times \ddot{\mathrm{F}}$
( $\ddot{r}=$ position vector; $\dot{\mathrm{p}}=$ linear momentum; $\ddot{\mathrm{L}}=$ angular momentum; $\ddot{\alpha}=$ angular acceleration; $\mathrm{I}=$ moment of inertia; $\ddot{\mathrm{F}}=$ force; $\mathrm{t}=$ time $)$
Choose the correct answer from the options given below:
Acetic acid dissociates 1.3%. What will be the pH of \(\frac {N}{10}\) solution of the acid.
Let z = x + iy be a complex number satisfying the following equation |z - (2 + i)| = |Re(z) - 4 | Which of the following options describes the above equation?
Rotational motion can be defined as the motion of an object around a circular path, in a fixed orbit.
The wheel or rotor of a motor, which appears in rotation motion problems, is a common example of the rotational motion of a rigid body.
Other examples: