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Consider a block kept on an inclined plane (inclined 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 friction between the block and inclined plane (\( \mu \)) is equal to:

A body of mass \(10 \, \text{kg}\) is moving with an initial speed of \(20 \, \text{m/s}\). The body stops after \(5 \, \text{s}\) due to friction between body and the floor. The value of the coefficient of friction is: (Take acceleration due to gravity \(g = 10 \, \text{m s}^{-2}\))

A bullet of \( 10 \, \text{g} \) leaves the barrel of gun with a velocity of \( 600 \, \text{m/s} \). If the barrel of gun is \( 50 \, \text{cm} \) long and mass of gun is \( 3 \, \text{kg} \), then value of impulse supplied to the gun will be:

\( 100 \) balls each of mass \( m \) moving with speed \( v \) simultaneously strike a wall normally and reflected back with same speed, in time \( t \, \text{s} \). the total force exerted by the balls on the wall is:

The position vector of a particle related to time \( t \) is given by \( \vec{r} = (10 t \hat{i} + 15 t^{2} \hat{j} + 7 \hat{k}) \, \text{m} \). The direction of net force experienced by the particle is:

As shown in figure, a \( 70 \, \text{kg} \) garden roller is pushed with a force of \( \vec{F} = 200 \, \text{N} \) at an angle of \( 30^\circ \) with horizontal. The normal on the roller is:
(Given \( g = 10 \, \text{m s}^{-2} \))

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 \( g = 10 \, \text{m} \, /\text{s}^{2} \))

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

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 standing on it is more than his/her weight when the elevator goes does with increasing speed.
In the light of the above statement, choose the correct answer form the options given below:

A stone is projected at angle \( 30^\circ \) to the horizontal. The ratio of kinetic energy of the stone at point of projection to its kinetic energy at the highest point of flight will be:

A stone of mass \( 1 \, \text{kg} \) is tied to end of a massless string of length \( 1 \, \text{m} \). If the breaking tension of the string is \( 400 \, \text{N} \), then maximum linear velocity, the stone can have without breaking the string, while rotating in horizontal plane, is:

A lift of mass \( M = 500 \, \text{kg} \) is descending with speed of \( 2 \, \text{m s}^{-1} \). Its supporting cable begins to slip thus allowing it to fall with a constant acceleration of \( 2 \, \text{m s}^{-2} \). The kinetic energy of the lift at the end of fall through to a distance of \( 6 \, \text{m} \) will be ______\( \text{kJ} \).

At any instant the velocity of a particle of mass \( 500 \, \text{g} \) is \( (2t\hat{i} + 3t^{2}\hat{j}) \, \text{ms}^{-1} \). If the force acting on the particle at \( t = 1 \, \text{s} \) is \( (\hat{i} + x\hat{j}) \, \text{N} \). Then the value of \( x \) will be:

A block of mass \( 5 \ \text{kg} \) is placed at rest on a table of rough surface. Now, if a force of \( 30 \ \text{N} \) is applied in the direction parallel to surface of the table, the block slides through a distance of \( 50 \ \text{m} \) in an interval of time \( 10 \ \text{s} \). Coefficient of kinetic friction is: (given \( g = 10 \ \text{m} / \text{s}^{2} \) )

A small block of mass \( 100 \, \text{g} \) is tied to a spring of spring constant \( 7.5 \, \text{N/m} \) and length \( 20 \, \text{cm} \). The other end of spring is fixed at a particular point A. If the block moves in a circular path on a smooth horizontal surface with constant angular velocity \( 5 \, \text{rad/s} \) about point A, then tension in the spring is:

A \( 0.4 \, \text{kg} \) mass takes \( 8 \, \text{s} \) to reach ground when dropped from a certain height ‘\( P \)’ above surface of earth. The loss of potential energy in the last second of fall is ______ \( \text{J} \). (Take \( g = 10 \, \text{m/s}^{2} \))

A car is moving with a constant speed of \( 20 \, \text{m/s} \) in a circular horizontal track of radius \( 40 \, \text{m} \). a bon is suspended from the roof of the car by a massless string. The angle made by the string with the vertical will be: (Take \( g = 10 \, \text{m/s}^2 \))

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