MCQ
The instantaneous angular position of a point on a rotating wheel is given by the equation $\theta(t)=2 t^3-6 t^2$. The torque on the wheel becomes zero at
  • A
    $t =0.25 s$
  • B
    $t =0.5 s$
  • C
    $t=2 s$
  • D
    $t=1 s$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

The coefficient of volumetric expansion of mercury is $18 × 10^{-5}{°C^{-1}}$. A thermometer bulb has a volume $10^{-6}\, m^3$ and cross section of stem is $ 0.004 \,cm^2$. Assuming that bulb is filled with mercury at $0°C$ then the length of the mercury column at $100°C$ is
Two cars $S_1$ and $S_2$ are moving in coplanar concentric circular tracks in the opposite sense with the periods of revolution $3 \,min$ and $24 \,min$, respectively. At time $t=0$, the cars are farthest apart. Then, the two cars will be 
A heavy solid sphere is thrown on a horizontal rough surface with initial velocity $u$ without rolling. What will be its speed, when it starts pure rolling motion?
A circular plate of diameter ' $a$ ' is kept in contact with a square plate of side $a$ as shown. The density of the material and the thickness are same everywhere. The centre of mass of composite system will be ...........
Two straight metallic strips each of thickness $t$ and length $\ell$ are rivetted together. Their coefficients of linear expansions are $\alpha_1$ and $\alpha_2$. If they are heated through temperature $\Delta T$, the bimetallic strip will bend to form an arc of radius
A bar of mas $M=1.00 \mathrm{~kg}$ and length $L=0.20 \mathrm{~m}$ is lying on a horizontal frictionless surface. One end of the bar is pivoted at a point about which it is free to rotate. A small mass $m=0.10 \mathrm{~kg}$ is moving on the same horizontal surface with $5.00 \mathrm{~m} \mathrm{~s}^{-1}$ speed on a path perpendicular to the bar. It hits the bar at a distance $L / 2$ from the pivoted end and returns back on the same path with speed $v$. After this elastic collision, the bar rotates with an angular velocity $\omega$. Which of the following statement is correct?
A ferromagnetic material is placed in an external magnetic field. The magnetic domains:
  1. Increase in size.
  2. Decrease in size.
  3. May increase or decrease in size.
  4. Have no relation with the field.
$A$ yo-yo is resting on a rough horizontal table. Forces $F_1, F_2$ and $F_3$ are applied separately as shown. The correct statement is
Two discs have moments of intertia ${I}_{1}$ and ${I}_{2}$ about their respective axes perpendicular to the plane and passing through the centre. They are rotating with angular speeds, $\omega_{1}$ and $\omega_{2}$ respectively and are brought into contact face to face with their axes of rotation coaxial. The loss in kinetic energy of the system in the process is given by :
A uniformly thick wheel with moment of inertia $I$ and radius $R$ is free to rotate about its centre of mass (see fig). A massless string is wrapped over its rim and two blocks of masses $\mathrm{m}_{1}$ and $\mathrm{m}_{2}\left(\mathrm{m}_{1}>\mathrm{m}_{2}\right)$ are attached to the ends of the string. The system is released from rest. The angular speed of the wheel when $\mathrm{m}_{1}$ descents by a distance $h$ is