Question
A spring when stretched by $2 \,mm$ its potential energy becomes $4 \,J$. If it is stretched by $10 \,mm$, its potential energy is equal to

Answer

(d)$U = \frac{1}{2}k{x^2}$ if $x $ becomes $ 5$  times then energy will become $25 $ times i.e. $4 \times 25 = 100\,J$

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

When a hydrogen atom going from $\mathrm{n}=2$ to $\mathrm{n}=1$ emits a photon, its recoil speed is $\frac{\mathrm{x}}{5} \mathrm{~m} / \mathrm{s}$. Where $\mathrm{x}=$ ___________. (Use : mass of hydrogen atom$\left.=1.6 \times 10^{-27 /} \ \mathrm{kg}\right)$
A car of mass $1000\,kg$ negotiates a banked curve of radius $90\,m$ on a fictionless road. If the banking angle is $45^o$, the speed of the car is ......... $ms^{-1}$
A $U-$shaped wire is dipped in a soap solution, and removed. The thin soap film formed between the wire and the light slider supports a weight of $1.5 \times 10^{-2}\; N$ (which includes the small weight of the slider). The length of the slider is $30 \;cm .$ What is the surface tension of the film?
The moment of inertia of uniform semicircular disc of mass $M$ and radius $r$ about a line perpendicular to the plane of the disc through the centre is
One mole of an ideal gas $(\gamma = 1.4)$ is adiabatically compressed so that its temperature rises from $27\,^oC$ to $35\,^oC$ . The change in the internal energy of the gas is  .... $J$. (given $R = 8.3\,J/mole-K$ )
A small block of mass $100\,g$ is tied to a spring of spring constant $7.5\,N / m$ and length $20\, cm$. The other end of spring is fixed at a particular point $A$. If the block moves in a circular path on a smooth horizontal surface with constant angular velocity $5\,rad / s$ about point $A$, then tension in the spring is $.........\,N$
A thin metal plate $P$ is inserted half way between the plates of a parallel plate capacitor of capacitance $C$ in such a way that it is parallel to the two plates. The capacitance now becomes
A man is slipping on a frictionless inclined plane and a bag falls down from the same height. Then the velocity of both is related as
$M$ grams of steam at $100^{\circ} \mathrm{C}$ is mixed with $200\; \mathrm{g}$ of ice at its melting point in a thermally insulated container. If it produces liquid water at $40^{\circ} \mathrm{C}$ [heat of vaporization of water is $540 \;cal/\mathrm{g}$ and heat of fusion of ice is $80 \;\text { cal/g }]$ the value of $\mathrm{M}$ is
A light ray from air is incident (as shown in figure) at one end of a glass fiber (refractive index $\mu = 1.5$) making an incidence angle of $60^o$ on the lateral surface, so that it undergoes a total internal reflection. How much time would it take to traverse the straight fiber of length $1 km$