MCQ
$A$ disc of radius $R$ is rolling purely on a flat horizontal surface, with a constant angular velocity. The angle between the velocity and acceleration vectors of point $P$ is
- Azero
- ✓$45^o$
- C$135^o$
- D$tan^{-1}(1/2)$
✓
Answer
Correct option: B.
$45^o$
b
$\mathrm{a}_{\mathrm{r}}=\mathrm{R} \omega^{2}$ (radial acceleration is directed towards centre at point $\mathrm{P}$.
$\mathrm{a}_{\mathrm{r}}=\mathrm{R} \omega^{2}$ (radial acceleration is directed towards centre at point $\mathrm{P}$.
$\cos \theta=\frac{v_{c m}}{v_{p}}=\frac{v_{c m}}{\sqrt{2} v_{c m}}=\frac{1}{\sqrt{2}}$
$\theta=45^{\circ}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
If $10000\, V$ is applied across an $X$ - ray tube, what will be the ratio of de-Broglie wavelength of the incident electrons to the shortest wavelength of $X$ - ray produced ($\frac{e}{m}$ for electron is $1.8 \times {10^{11}}\,c\,k{g^{ - 1}}$)
→Two drops of the same radius are falling through air with a steady velocity of $5 cm per sec.$ If the two drops coalesce, the terminal velocity would be
→Pick out the statement which is not true
Some laws/processes are given in Column $I$. Match these with the physical phenomena given in Column $II$ and indicate your answer by darkening appropriate bubbles in the $4 \times 4$ matrix given in the $ORS$.
→| Column $I$ | Column $II$ |
| $(A)$ Transition between two atomic energy levels | $(p)$ Characteristic $X$-rays |
| $(B)$ Electron emission from a material | $(q)$ Photoelectric effect |
| $(C)$ Mosley's law | $(r)$ Hydrogen spectrum |
| $(D)$ Change of photon energy into kinetic energy of electrons | $(s)$ $\beta$-decay |
The reading of spring balance when a block is suspended from it in air, is $60\,N$. This reading is changed to $40\, N$ when the block is immersed in water. The specific density of the block is
→A red $LED$ emits light at $0.1$ watt uniformly around it. The amplitude of the electric field of the light at a distance of $1\ m$ from the diode is....$ Vm^{-1}$
→A mass $m$ , travelling at speed $V_0$ in a straight line from far away is deflected when it passes near a black hole of mass $M$ which is at a perpendicular distance $R$ from the original line of flight. $a$ , the distance of closest approach between the mass and the black hole is given by the relation
→A circular coil of $1000 \,\,turns$ each with area $1\, m ^{2}$ is rotated about its vertical diameter at the rate of one revolution per second in a uniform horizontal magnetic field of $0.07 \,T$. The maximum voltage generation will be......... $V$.
→A solid cylinder $P$ rolls without slipping from rest down an inclined plane attaining a speed $v_p$ at the bottom. Another smooth solid cylinder $Q$ of same mass and dimensions slides without friction from rest down the inclined plane attaining a speed $v_q$ at the bottom. The ratio of the speeds $\frac{v_q}{v_p}$ is
→In a series $R L C$ circuit, potential differences across $R, L$ and $C$ are $30 \,V , 60 \,V$ and $100 \,V$ respectively as shown in figure. The $e.m.f.$ of source (in volts) is .........
→