Exercise 1

An elastic spring under tension of $3 \mathrm{N}$ has length $a$. Its length is $b$ under tension $\text{2 N}$. For its length$(3\mathrm{a} – 2\mathrm{b}),$ the value of tension will be_____ $\mathrm{N}.$

A heavy box of mass 50 kg is moving on a horizontal surface. If co-efficient of kinetic friction between the box and horizontal surface is 0.3 then force of kinetic friction is :

A light string passing over a smooth light pulley connects two blocks of masses ${\mathrm{m}}_1$ and ${\mathrm{m}}_2$ (where ${\mathrm{m}}_2>{\mathrm{m}}_1$). If the acceleration of the system is $\frac{\mathrm{g}}{\sqrt{2}}$, then the ratio of the masses $\frac{{\mathrm{m}}_1}{ {\mathrm{m}}_2}$ is:

$$\begin{gathered} A massless spring gets elongated by amount x_1 \\ under a tension of 5N. Its elongation is x_2 under the \\ tension of 7N. For the elongation of \\ (5x_1 -2x_2), the tension in the spring will be, \end{gathered}$$

$\mathrm{A} \mathrm{car} \mathrm{of} \mathrm{mass} \text{'}\mathrm{m}\text{'} \mathrm{moves} \mathrm{on} \mathrm{a} \mathrm{banked} \mathrm{road} \mathrm{having} \mathrm{radius} \text{'}\mathrm{r}\text{'} \mathrm{and} \mathrm{banking} \mathrm{angle} \mathrm{\theta }. \mathrm{To} \mathrm{avoid} \mathrm{slipping} \mathrm{from} \mathrm{banked} \mathrm{road}, \mathrm{the} \mathrm{maximum} \mathrm{permissible} \mathrm{speed} \mathrm{of} \mathrm{the} \mathrm{car} \mathrm{is} {\mathrm{v}}_0. \mathrm{The} \mathrm{coefficient} \mathrm{of} \mathrm{friction} \mathrm{\mu } \mathrm{between} \mathrm{the} \mathrm{wheels} \mathrm{of} \mathrm{the} \mathrm{car} \mathrm{and} \mathrm{the} \mathrm{banked} \mathrm{road} \mathrm{is} :-$

$$\begin{gathered} A string of length L is fixed at one end and carries \\ a mass of M at the other end. The mass makes \\ \left(\frac{3}{\mathrm{\pi }}\right) rotations per second about the vertical axis \\ pas\sin g through end of the string as shown. The \\ tension in the string is \_\_\_\_\_ML. \end{gathered}$$

$$\begin{gathered} \mathrm{A} \mathrm{uniform} \mathrm{rod} \mathrm{of} \mathrm{mass} 250 \mathrm{g} \mathrm{having} \mathrm{length} 100 \mathrm{cm} \mathrm{is} \mathrm{balanced} \mathrm{on} \mathrm{a} \mathrm{sharp} \mathrm{edge} \mathrm{at} 40 \mathrm{cm} \mathrm{mark}. \mathrm{A} \mathrm{mass} \\ \mathrm{of} 400 \mathrm{g} \mathrm{is} \mathrm{suspended} \mathrm{at} 10 \mathrm{cm} \mathrm{mark}. \mathrm{To} \mathrm{maintain} \mathrm{the} \mathrm{balance} \mathrm{of} \mathrm{the} \mathrm{rod}, \mathrm{the} \mathrm{mass} \mathrm{to} \mathrm{be} \mathrm{suspended} \mathrm{at} \\ 90 \mathrm{cm} \mathrm{mark}, \mathrm{is} \end{gathered}$$

$$\begin{gathered} \mathrm{A} \mathrm{balloon} \mathrm{and} \mathrm{its} \mathrm{content} \mathrm{having} \mathrm{mass} \mathrm{M} \mathrm{is} \mathrm{A} \mathrm{balloon} \mathrm{and} \mathrm{its} \mathrm{content} \mathrm{having} \mathrm{mass} \mathrm{M} \mathrm{is} \mathrm{must} \mathrm{be} \mathrm{released} \mathrm{from} \mathrm{the} \mathrm{content} \mathrm{so} \mathrm{that} \mathrm{the} \\ \mathrm{balloon} \mathrm{starts} \mathrm{moving} \mathrm{up} \mathrm{with} \mathrm{an} \mathrm{acceleration} \text{'}3\mathrm{a}\text{'} \mathrm{will} \mathrm{be}: (\mathrm{Take} \text{'}\mathrm{g}\text{'} \mathrm{as} \mathrm{acceleration} \mathrm{due} \mathrm{to} \mathrm{gravity}) \end{gathered}$$