MCQ
$A$ solid uniform disk of mass $m$ rolls without slipping down a fixed inclined plane with an acceleration $a$. The frictional force on the disk due to surface of the plane is :
- A$2\, ma$
- B$3/2\, ma$
- C$ma$
- ✓$1/2\, ma$
✓
Answer
Correct option: D.
$1/2\, ma$
d
Here as the sphere is rolling down an inclined plane it will produce a torque $\tau=I \alpha$
Here as the sphere is rolling down an inclined plane it will produce a torque $\tau=I \alpha$
where $1=$ moment of inertia and $\alpha=$ angular acceleration
Now the frictional force $f=N \mu_{s}$
Where $\mathrm{N}=$ normal force $=m g \cos \theta$ and $\mu_{s}=$ static friction
We also know moment of inertia of sphere $I=\frac{1}{2} m R^{2}$ 'where Reradius of sphere.
and $\alpha=\frac{\text {acceleration}(a)}{R}$
In the given case torque $\tau$ = frictional force $f \times R$
$f R=I \tau$
$f R=\frac{1}{2} m R^{2} \frac{a}{R}$
$f=\frac{m a}{2}$
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
A circular metallic ring of radius $R$ has a small gap of width $d$. The coefficient of thermal expansion of the metal is $\alpha$ in appropriate units. If we increase the temperature of the ring by an amount $\Delta T$, then width of the gap
→A fly wheel of moment of inertia $0.4\,\, kg\, m^2$ and radius $0.2\,\, m$ is free to rotate about a central axis. If a string is wrapped around it and it is pulled with a force of $10 \,N$ , then angular velocity after $4\,\, sec$ will be ......... $rad\,\,s^{-1}$.
→Kinetic theory of gases provide a base for
To which country, scientist J.J. Thomson belong?
A van der Waal's gas obeys the equation of state $\left(p+\frac{n^2 a}{V^2}\right)(V-n b)=n R T$. Its internal energy is given by $U=C T-\frac{n^2 a}{V}$. The equation of a quasistatic adiabat for this gas is given by
→Four curves $A, B, C$ and $D$ are drawn in the adjoining figure for a given amount of gas. The curves which represent adiabatic and isothermal changes are
→Wind is blowing in the north direction at speed of $2 \,\,m/s$ which causes the rain to fall at some angle with the vertical. With what velocity should a cyclist drive so that the rain appears vertical to him :
→The velocity at the maximum height of a projectile is half of its initial velocity $u$. Its range on the horizontal plane is
→What is the phase difference between the displacement wave and pressure wave in sound wave?
A block of mass $m$ lying on a rough horizontal plane is acted upon by a horizontal force $P$ and another force $Q$ inclined at an angle $\theta $ to the vertical. The block will remain in equilibrium, if the coefficient of friction between it and the surface is
→