A solid sphere of mass 2 kg is rolling on a friction horizontal s… - Vidyadip

MCQ

A solid sphere of mass $2 kg$ is rolling on a friction horizontal surface with velocity $6 m / s$. It collides on the free end of an ideal spring whose other end is fixed. The maximum compression produced in the spring will be (Force constant of the spring - $36 N / m$ ).

A
$\sqrt{14} m$
✓
$\sqrt{2.8} m$
C
$\sqrt{1.4} m$
D
$\sqrt{0.7} m$

✓

Answer

Correct option: B.

$\sqrt{2.8} m$

(b) : Kinetic energy of rolling solid sphere
$
\begin{aligned}

& =\frac{1}{2} m v^2+\frac{1}{2} I \omega^2=\frac{1}{2} m v^2+\frac{1}{2} \times \frac{2}{5} m r^2 \omega^2 \\

& =\frac{1}{2} m v^2+\frac{1}{5} m v^2=\frac{7}{10} m v^2 \\
& =\frac{7}{10} \times 2 \times(6)^2=\frac{7}{10} \times 2 \times 36=\frac{252}{5}
\end{aligned}
$
The potential energy of the spring of maximum compression $x=\frac{1}{2} k x^2$

or $\frac{1}{2} k x^2=\frac{252}{5}$ or $k x^2=\frac{252 \times 2}{5}$

or $\quad x^2=\frac{252 \times 2}{5 \times 36}=2.8 \quad$ or $\quad x=\sqrt{2.8} m$

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

Explore more

More "M.C.Q (1 Marks)" from Rotational Dynamics→Rotational Dynamics — all question types→Physics STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

In a second’s pendulum, the mass of Bob is 50 g. If it is replaced by 100 g mass, then its period will be ______.

A fluid flows past a sphere in streamline flow. The viscous force on the sphere is directly proportional to

The ratio of magnetic dipole moment of an electron of charge $e$ and mass $m$ in Bohr's orbit in hydrogen atom to its angular momentum is

A current of $1 A$ is flowing on the sides of an equilateral triangle of side $4.5 \times 10^{-2} m$. The magnetic field at the centre of the triangle will be

With a resistance of X in the left gap and a resistance of 9 $\Omega$ in the right gap of a meter bridge, the balance point is obtained at 40 cm from the left end. In what way and to which resistance 3 $\Omega$ resistance to be connected to obtain the balance at 50 cm from the left end?

At constant temperature, increasing the pressure of a gas by $5 \%$ its volume will decrease by

In biprism experiment, the distance of 20th bright band from the central bright band is 1.2 cm. Without changing the experimental set-up, the distance of 30 bright band from the central bright band will be ______.

The value of current $i_1$ flowing from $A$ to $C$ in the circuit diagram is

→

In a gravity free space, the liquid in a capillary tube will rise to

A paralel-plate capacitor is charged by connecting it to a battery. The battery is then disconnected and the distance between the plates is doubled. This doubles