Telangana Board Solutions for Chapter: Laws of Motion, Exercise 1: EXERCISES

A fixed pulley with a smooth groove has a light string passing over it with a $4 \mathrm{kg}$ attached on one side and a $3 \mathrm{kg}$ on the other side. Another $3 \mathrm{kg}$ is hung from the other $3 \mathrm{kg}$ as shown with another light string. If the system is released from rest, find the common acceleration (in $\mathrm{m} {\mathrm{s}}^{-2}$).

(Take, $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

A block of mass 2 kg slides on an inclined plane that makes an angle of 30 degree with the horizontal. The coefficient of friction between the block and the surface is $\frac{\sqrt{3}}{2}$. What force (in Newton) should be applied to the block so that it moves down without any acceleration? ($g=9.8 \mathrm{m}/{\mathrm{s}}^2$)

A block of mass 2 kg slides on an inclined plane that makes an angle of 30 degree with the horizontal. The coefficient of friction between the block and the surface is $\frac{\sqrt{3}}{2}$. What force (in Newton) should be applied to the block so that it moves up without any acceleration? ($g=9.8 \mathrm{m}/{\mathrm{s}}^2$)

A block is placed on a ramp of parabolic shape given by the equation $y=\frac{x^2}{20}$. If $\mu =0.5$, what is the maximum height above the ground at which the block can be placed without slipping? 

A block of metal of mass $2 \mathrm{kg}$ on a horizontal table is attached to a mass of $0.45 \mathrm{kg}$ by a light string passing over a frictionless pulley at the edge of the table.The block is subjected to a horizontal force by allowing the $0.45 \mathrm{kg}$ mass to fall. The coefficient of sliding friction between the block and table is $0.2$. Calculate the initial acceleration (in $\mathrm{m}/{\mathrm{s}}^2$). ($g=10 \mathrm{m}/{\mathrm{s}}^2$)

A block of metal of mass $2 \mathrm{kg}$ on a horizontal table is attached to a mass of $0.45 \mathrm{kg}$ by a light string passing over a frictionless pulley at the edge of the table.The block is subjected to a horizontal force by allowing the $0.45 \mathrm{kg}$ mass to fall. The coefficient of sliding friction between the block and table is $0.2$. Calculate the tension (in Newton) in the string. ($g=10 \mathrm{m}/{\mathrm{s}}^2$)

A block of metal of mass $2 \mathrm{kg}$ on a horizontal table is attached to a mass of $0.45 \mathrm{kg}$ by a light string passing over a frictionless pulley at the edge of the table.The block is subjected to a horizontal force by allowing the $0.45 \mathrm{kg}$ mass to fall. The coefficient of sliding friction between the block and table is $0.2$. Calculate the distance (in metres) the block would continue to move if, after $2$ seconds of motion, the string should break. ($g=10 \mathrm{m}/{\mathrm{s}}^2$)

On a smooth horizontal surface a block A of mass $10 \mathrm{kg}$ is kept. On this block a second block B of mass $5 \mathrm{kg}$ is kept. The coefficient of friction between the two blocks is $0.4$. A horizontal force of $30 \mathrm{N}$ is applied on the lower block as shown. The force of friction between the blocks is 

($g=10 \mathrm{m}/{\mathrm{s}}^2$)