$\mathrm{Which} \mathrm{is} \mathrm{true} \mathrm{for} \mathrm{rolling} \mathrm{frictrion} \left( {\mathrm{\mu }}_{\mathrm{r} }\right), \mathrm{static} \mathrm{friction}\left( {\mathrm{\mu }}_{\mathrm{s}} \right) \mathrm{and} \mathrm{kinetic} \mathrm{friction} \left( {\mathrm{\mu }}_{\mathrm{k} }\right):$

• ${\mathrm{\mu }}_{\mathrm{s}} > {\mathrm{\mu }}_{\mathrm{k}} > {\mathrm{\mu }}_{\mathrm{r}}$

• ${\mathrm{\mu }}_{\mathrm{s}} < {\mathrm{\mu }}_{\mathrm{k}} < {\mathrm{\mu }}_{\mathrm{r}}$

• ${\mathrm{\mu }}_{\mathrm{s}} < {\mathrm{\mu }}_{\mathrm{k}} > {\mathrm{\mu }}_{\mathrm{r}}$

• ${\mathrm{\mu }}_{\mathrm{s}} > {\mathrm{\mu }}_{\mathrm{r} } > {\mathrm{\mu }}_{\mathrm{k}}$

Two weights w₁ and w₂ are suspended to the two strings on a frictionless pulley. When the pulley is pulled up with an acceleration g, then the tension in the string is :

Two similar charges having mass m and 2m are placed in an electric field. The ratio of their kinetic energy is :

• 4:1

• 1:1

• 2:1

• 1:2

4.

In a system of units if force (F), acceleration (A), and time (T) are taken as fundamental units, then the dimensional formula of energy is:

• FA²T

• FAT²

• F²AT

• FAT

A car starts from rest, moves with an acceleration a and then decelerates at a constant rate b for sometimes to come to rest. If the total time taken is t. The maximum velocity of car is given by :

• $\frac{\mathrm{a} \mathrm{b} \mathrm{t}}{\left(\mathrm{a} + \mathrm{b} \right)}$

• $\frac{{\mathrm{a}}^2 \mathrm{t}}{\mathrm{a} + \mathrm{b}}$

• $\frac{\mathrm{a} \mathrm{t}}{\left(\mathrm{a}+ \mathrm{b}\right)}$

• $\frac{{\mathrm{b}}^2 \mathrm{t}}{\mathrm{a}+\mathrm{b}}$

Two planets are revolving around the earth with velocities v₁ and v₂ and in radii r₁ and r₂ ( r₁ > r₂ ) respectively. Then :

• v₁ = v₂

• v₁ > v₂

• v₁ < v₂

• $\frac{{\mathrm{v}}_1}{{\mathrm{r}}_1} =\frac{{\mathrm{v}}_2}{{\mathrm{r}}_2}$

The angular momentum of a rotating body changes from A_o to 4A_o in 4 minutes. The torque acting on the body is:

• 3/4 A_o

• 4A_o

• 3A_o

• 3/2A_o

Earth is revolving around the sun. If the distance of the earth from the sun is reduced to 1/4th of the present distance then the length of present day will be reduced by :

• $\frac{1}{4}$

• $\frac{1}{2}$

• $\frac{1}{8}$

• $\frac{1}{6}$

There are two planets and the ratio of radius of the two planets is K but ratio of acceleration due to gravity of both planets is g. What will be the ratio of their escape velocity ?

• (kg)^1/2

• (kg)^-1/2

• (kg)²

• (kg)^-2

If a spherical ball rolls on a table without slipping the friction of its total energy associated with rotational energy is :

• 3/5

• 2/7

• 2/5

• 3/7