Laws of Motion

A block rests on a rough inclined plane `making an angle of ${30^ \circ }$ with the horizontal. The coefficient of static friction between the block and the plane is $0.8.$ If the frictionless force on the block is $10$ $N,$ the mass of the block (in $kg$) is $\left( {take\,\,\,g\, = \,10\,\,m/{s^2}} \right)$

A force acts for 20 s on a body of mass 20 kg, starting from rest, after which the force ceases and then body describes 50 m in the next 10 s. The value of force will be:

A spring whose unstretched length is l has a force constant k. The spring is cut into two pieces of unstretched lengths l₁ and l₂ where, l₁ = nl₂ and n is an integer. The ratio k₁/k₂ of the corresponding force constant, k₁ and k₂ will be :

A marble block of mass $2$ $kg$ lying on ice when given a velocity of $6$ $m/s$ is stopped by friction in $10$ $s.$ Then the coefficient of friction is

When forces ${F_1},\,\,{F_2},\,\,{F_3}$ are acting on a particle of mass $m$ such that ${F_2}$ and ${F_3}$ are mutually perpendicular, then the particle remains stationary. If the force ${F_1}$ is now removed then the acceleration of the particle is

A mass of 10 kg is suspended vertically by a rope from the roof. When a horizontal force is applied on the rope at some point. the rope deviated at an angle of 45^o at the roof point. If the suspended mass is at equilibrium, the magnitude of the force applied is (g = 10 ms^$-$2

A mass of 10 kg is suspended by a rope of length 4 m, from the ceiling. A force F is applied horizontally at the mid point of the rope such that the top half of the rope makes an angle of 45^o with the vertical. Then F equal : (Take g = 10 ms^–2 and the rope to be massless)

Statement : 1 If three forces ${\overrightarrow F _1},{\overrightarrow F _2}$ and ${\overrightarrow F _3}$ are represented by three sides of a triangle and ${\overrightarrow F _1} + {\overrightarrow F _2} = - {\overrightarrow F _3}$, then these three forces are concurrent forces and satisfy the condition for equilibrium. Statement : 2 A triangle made up of three forces ${\overrightarrow F _1}$, ${\overrightarrow F _2}$ and ${\overrightarrow F _3}$ as its sides taken in the same order, satisfy the condition for translatory equilibrium. In the light of the above statements, choose the most appropriate answer from the options given below :

Three forces $F_{1}=10 \mathrm{~N}, F_{2}=8 \mathrm{~N}, \mathrm{~F}_{3}=6 \mathrm{~N}$ are acting on a particle of mass $5 \mathrm{~kg}$. The forces $\mathrm{F}_{2}$ and $\mathrm{F}_{3}$ are applied perpendicularly so that particle remains at rest. If the force $F_{1}$ is removed, then the acceleration of the particle is:

A heavy iron bar, of weight $W$ is having its one end on the ground and the other on the shoulder of a person. The bar makes an angle $\theta$ with the horizontal. The weight experienced by the person is :

A body of weight $200 \mathrm{~N}$ is suspended from a tree branch through a chain of mass $10 \mathrm{~kg}$. The branch pulls the chain by a force equal to (if $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$) :

A smooth block is released at rest on a ${45^ \circ }$ incline and then slides a distance $'d'$. The time taken to slide is $'n'$ times as much to slide on rough incline than on a smooth incline. The coefficient of friction is

Consider a car moving on a straight road with a speed of $100$ $m/s$. The distance at which car can be stopped is $\left[ {{\mu _k} = 0.5} \right]$

A block of mass $m$ is placed on a surface with a vertical cross section given by $y = {{{x^3}} \over 6}.$ If the coefficient of friction is $0.5,$ the maximum height above the ground at which the block can be placed without slipping is:

A rocket is fired vertically from the earth with an acceleration of 2g, where g is the gravitational acceleration. On an inclined plane inside the rocket, making an angle $\theta$ with the horizontal, a point object of mass m is kept. The minimum coefficient of friction $\mu$_min between the mass and the inclined surface such that the mass does not move is :

A given object takes n times more time to slide down a ${45^ \circ }$ rough inclined plane as it takes to slide down a perfectly smooth ${45^ \circ }$ incline. The coefficient of kinetic friction between the object and the incline is :

A body of mass 2 kg slides down with an acceleration of 3 m/s² on a rough inclined plane having a slope of ${30^o}$. The external force required to take the same body up the plane with the same acceleration will be : (g = 10 m/s²)

An insect is at the bottom of a hemispherical ditch of radius 1 m. It crawls up the ditch but starts slipping after it is at height h from the bottom. If the coefficient of friction between the ground and the insect is 0.75, then h is : (g = 10 ms^–2)

A block of mass 10 kg starts sliding on a surface with an initial velocity of 9.8 ms^$-$1. The coefficient of friction between the surface and block is 0.5. The distance covered by the block before coming to rest is : [use g = 9.8 ms^$-$2]