Laws of Motion

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:

Consider a block kept on an inclined plane (incline at 45\(^\circ\)) as shown in the figure. If the force required to just push it up the incline is 2 times the force required to just prevent it from sliding down, the coefficient of frictio...

Given below are two statements :
Statement I : An elevator can go up or down with uniform speed when its weight is balanced with the tension of its cable.
Statement II : Force exerted by the floor of an elevator on the foot of a person stan...

As per given figure, a weightless pulley P is attached on a double inclined frictionless surfaces. The tension in the string (massless) will be (if g = 10 m/s\(^2\))

A block of mass \(5 \mathrm{~kg}\) is placed at rest on a table of rough surface. Now, if a force of \(30 \mathrm{~N}\) is applied in the direction parallel to surface of the table, the block slides through a distance of \(50 \mathrm{~m}\) ...

Figures (a), (b), (c) and (d) show variation of force with time.

The impulse is highest in figure.

As shown in the figure a block of mass 10 kg lying on a horizontal surface is pulled by a force F acting at an angle \(30^\circ\), with horizontal. For \(\mu_s=0.25\), the block will just start to move for the value of F : [Given $$g=10~\ma...

The position vector of a particle related to time $t$ is given by

$\vec{r}=\left(10 t \hat{i}+15 t^{2} \hat{j}+7 \hat{k}\right) m$

The direction of net force experienced by the particle is :

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...

A body of mass \(500 \mathrm{~g}\) moves along \(\mathrm{x}\)-axis such that it's velocity varies with displacement \(\mathrm{x}\) according to the relation \(v=10 \sqrt{x} \mathrm{~m} / \mathrm{s}\) the force acting on the body is:-

A 2 kg block is pushed against a vertical wall by applying a horizontal force of 50 N. The coefficient of static friction between the block and the wall is 0.5. A force F is also applied on the block vertically upward (as shown in figure). ...

A block of mass M placed inside a box descends vertically with acceleration 'a'. The block exerts a force equal to one-fourth of its weight on the floor of the box. The value of 'a' will be

A block of mass 40 kg slides over a surface, when a mass of 4 kg is suspended through an inextensible massless string passing over frictionless pulley as shown below.
The coefficient of kinetic friction between the surface and block is 0.02...

Two bodies of masses \(m_{1}=5 \mathrm{~kg}\) and \(m_{2}=3 \mathrm{~kg}\) are connected by a light string going over a smooth light pulley on a smooth inclined plane as shown in the figure. The system is at rest. The force exerted by the i...

A hanging mass M is connected to a four times bigger mass by using a string-pulley arrangement, as shown in the figure. The bigger mass is placed on a horizontal ice-slab and being pulled by 2 Mg force. In this situation, tension in the str...

A block of mass 2 kg moving on a horizontal surface with speed of 4 ms\(-\)1 enters a rough surface ranging from x = 0.5 m to x = 1.5 m. The retarding force in this range of rough surface is related to distance by F = \(-\)kx where k = 12 N...

A uniform metal chain of mass m and length 'L' passes over a massless and frictionless pulley. It is released from rest with a part of its length 'l' is hanging on one side and rest of its length '\(\mathrm{L}-l\)' is hanging on the other s...

A system of two blocks of masses m = 2 kg and M = 8 kg is placed on a smooth table as shown in figure. The coefficient of static friction between two blocks is 0.5. The maximum horizontal force F that can be applied to the block of mass M s...

A mass of 10 kg is suspended vertically by a rope of length 5 m from the roof. A force of 30 N is applied at the middle point of rope in horizontal direction. The angle made by upper half of the rope with vertical is \(\theta\) = tan\(-\)1...

A bag is gently dropped on a conveyor belt moving at a speed of \(2 \mathrm{~m} / \mathrm{s}\). The coefficient of friction between the conveyor belt and bag is \(0.4\). Initially, the bag slips on the belt before it stops due to friction. ...

Two inclined planes are placed as shown in figure. A block is projected from the Point A of inclined plane AB along its surface with a velocity just sufficient to carry it to the top Point B at a height 10 m. After reaching the Point B the ...

A block 'A' takes 2 s to slide down a frictionless incline of 30\(^\circ\) and length 'l', kept inside a lift going up with uniform velocity 'v'. If the incline is changed to 45\(^\circ\), the time taken by the block, to slide down the incl...

A block of mass M slides down on a rough inclined plane with constant velocity. The angle made by the incline plane with horizontal is \(\theta\). The magnitude of the contact force will be :

A person is standing in an elevator. In which situation, he experiences weight loss?

A system to 10 balls each of mass 2 kg are connected via massless and unstretchable string. The system is allowed to slip over the edge of a smooth table as shown in figure. Tension on the string between the 7th and 8th ball is __________ N...

In the arrangement shown in figure a1, a2, a3 and a4 are the accelerations of masses m1, m2, m3 and m4 respectively. Which of the following relation is true for this arrangement?

A monkey of mass \(50 \mathrm{~kg}\) climbs on a rope which can withstand the tension (T) of \(350 \mathrm{~N}\). If monkey initially climbs down with an acceleration of \(4 \mathrm{~m} / \mathrm{s}^{2}\) and then climbs up with an accelera...

Three masses \(M=100 \mathrm{~kg}, \mathrm{~m}_{1}=10 \mathrm{~kg}\) and \(\mathrm{m}_{2}=20 \mathrm{~kg}\) are arranged in a system as shown in figure. All the surfaces are frictionless and strings are inextensible and weightless. The pull...

Two masses \(M_{1}\) and \(M_{2}\) are tied together at the two ends of a light inextensible string that passes over a frictionless pulley. When the mass \(M_{2}\) is twice that of \(M_{1}\), the acceleration of the system is \(a_{1}\). Whe...

A force on an object of mass 100 g is \(\left( {10\widehat i + 5\widehat j} \right)\) N. The position of that object at t = 2 s is \(\left( {a\widehat i + b\widehat j} \right)\) m after starting from rest. The value of \({a \over b}\) will ...

A block of mass 200 g is kept stationary on a smooth inclined plane by applying a minimum horizontal force F = \(\sqrt{x}\)N as shown in figure.

The value of x = _____________.

Four forces are acting at a point \(\mathrm{P}\) in equilibrium as shown in figure. The ratio of force \(\mathrm{F}_{1}\) to \(\mathrm{F}_{2}\) is \(1: x\) where \(x=\) _____________.

For a free body diagram shown in the figure, the four forces are applied in the 'x' and 'y' directions. What additional force must be applied and at what angle with positive x-axis so that the net acceleration of body is zero?

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...

An object of mass 5 kg is thrown vertically upwards from the ground. The air resistance produces a constant retarding force of 10 N throughout the motion. The ratio of time of ascent to the time of descent will be equal to : [Use g = 10 ms$...

A car is moving on a plane inclined at 30\(^\circ\) to the horizontal with an acceleration of 10 ms\(-\)2 parallel to the plane upward. A bob is suspended by a string from the roof of the car. The angle in degrees which the string makes wit...

Statement : 1If three forces \({\overrightarrow F _1},{\overrightarrow F _2}\) and \({\overrightarrow F _3}\) are represented by three sides of a triangle and \({\overrightarrow F _1} + {\overrightarrow F _2} = - {\overrightarrow F _3}\), ...

A particle of mass M originally at rest is subjected to a force whose direction is constant but magnitude varies with time according to the relation \(F = {F_0}\left[ {1 - {{\left( {{{t - T} \over T}} \right)}^2}} \right]\)Where F0 and T ar...

The boxes of masse 2 kg and 8 kg are connected by a massless string passing over smooth pulleys. Calculate the time taken by box of mass 8 kg to strike the ground starting from rest. (use g = 10 m/s2)

As shown in the figure, a block of mass \(\sqrt 3\) kg is kept on a horizontal rough surface of coefficient of friction \({1 \over {3\sqrt 3 }}\). The critical force to be applied on the vertical surface as shown at an angle 60\(^\circ\) w...

A person standing on a spring balance inside a stationary lift measures 60 kg. The weight of that person if the lift descends with uniform downward acceleration of 1.8 m/s2 will be ______________ N. [g = 10 m/s2]

A boy pushes a box of mass 2 kg with a force \(\overrightarrow F = \left( {20\widehat i + 10\widehat j} \right)N\) on a frictionless surface. If the box was initially at rest, then ___________ m is displacement along the x-axis after 10s.

Two masses A and B, each of mass M are fixed together by a massless spring. A force acts on the mass B as shown in the figure. If the mass A starts moving away from mass B with acceleration 'a', then the acceleration of mass B will be :

The initial mass of a rocket is 1000 kg. Calculate at what rate the fuel should be burnt so that the rocket is given an acceleration of 20 ms-2. The gases come out at a relative speed of 500 ms\(-\)1 with respect to the rocket : [Use g = 10...

The coefficient of static friction between two blocks is 0.5 and the table is smooth. The maximum horizontal force that can be applied to move the blocks together is .................. N. (take g = 10 ms-2)

A force \(\overrightarrow F = (40\widehat i + 10\widehat j)N\) acts on a body of mass 5 kg. If the body starts from rest, its position vector \(\overrightarrow r\) at time t = 10 s, will be :

The coefficient of static friction between a wooden block of mass 0.5 kg and a vertical rough wall is 0.2. The magnitude of horizontal force that should be applied on the block to keep it adhere to the wall will be _________ N. [g = 10 ms$$...

An inclined plane is bent in such a way that the vertical cross-section is given by \(y = {{{x^2}} \over 4}\) where y is in vertical and x in horizontal direction. If the upper surface of this curved plane is rough with coefficient of frict...

A particle is projected with velocity v0 along x-axis. A damping force is acting on the particle which is proportional to the square of the distance from the origin i.e. ma = \(-\) \(\alpha\)x2. The distance at which the particle stops :

A steel block of 10 kg rests on a horizontal floor as shown. When three iron cylinders are placed on it as shown, the block and cylinders go down with an acceleration 0.2 m/s2. The normal reaction R' by the floor if mass of the iron cylinde...