An open knife edge of mass 'm' is dropped from a height 'h' on a wooden floor. If the blade penetrates upto the depth 'd' into the wood, the average resistance offered by the wood to the knife edge is 

A body is moving along a straight line by a machine delivering constant power. The distance moved by the body in time t is proportional to 

A batsman hits a sixer and the ball touches the ground outside the cricket field. Which of the following graph describes the variation of the cricket ball's vertical velocity v with time between the time t₁ as it hits the bat and time t₂ when it touches the ground 

The relationship between force and position is shown in the given figure (in a one-dimensional case). The work done by the force in displacing a body from x = 1 cm to x = 5 cm is:

The pointer reading v/s load graph for a spring balance is as given in the figure. The spring constant is-

Adjacent figure shows the force-displacement graph of a moving body, the work done in displacing body from x = 0 to x = 35 m is equal to-

A 10kg mass moves along x-axis. Its acceleration as a function of its position is shown in the figure. What is the total work done on the mass by the force as the mass moves from x = 0 to x = 8 cm ?

A toy car of mass 5 kg moves up a ramp under the influence of force F plotted against displacement x. The maximum height attained is given by

The graph between the resistive force F acting on a body and the distance covered by the body is shown in the figure. The mass of the body is 25 kg and the initial velocity is 2 m/s. When the distance covered by the body is 4m, its kinetic energy would be:

A particle of mass 0.1 kg is subjected to a force which varies with distance as shown in fig. If it starts its journey from rest at x = 0 , its velocity at x = 12 m is 

The relation between the displacement X of an object produced by the application of the variable force F is represented by a graph shown in the figure. If the object undergoes a displacement from X = 0.5 m to X = 2.5 m the work done will be approximately equal to 

A particle is given a constant horizontal velocity  from height h. Taking g to be constant every where, kinetic energy E of the particle w. r. t. time t is correctly shown in

The adjoining diagram shows the velocity versus time plot for a particle. The work done by the force on the particle is positive from

A particle which is constrained to move along the x-axis, is subjected to a force in the same direction which varies with the distance x of the particle from the origin as $F\left(x\right)=-kx+a{x}^3$. Here k and a are positive constants. For $x\ge 0$, the functional form of the potential energy U(x) of the particle is-

A force F acting on an object varies with distance x as shown here. The force is in newton and x in metre. The work done by the force in moving the object from x = 0 to x = 6 m is 

The potential energy of a system is represented in the first figure. the force acting on the system will be represented by

A particle, initially at rest on a frictionless horizontal surface, is acted upon by a horizontal force which is constant in size and direction. A graph is plotted between the work done (W) on the particle, against the speed of the particle, (v). If there are no other horizontal forces acting on the particle the graph would look like

Which of the following graphs is correct between kinetic energy (E), potential energy (U) and height (h) from the ground of the particle

The force acting on a body moving along x-axis varies with the position of the particle as shown in the fig.

The body is in stable equilibrium at

The potential energy of a particle varies with distance x as shown in the graph. The force acting on the particle is zero at

Figure shows the F-x graph. Where F is the force applied and x is the distance covered by the body along a straight line path. Given that F is in newton and x in metre, what is the work done ?

The force required to stretch a spring varies with the distance as shown in the figure. If the experiment is performed with the above spring of half length, the line OA will

The graph between E and v is

A body moves from rest with a constant acceleration. Which one of the following graphs represents the variation of its kinetic energy K with the distance travelled x ?

The diagrams represent the potential energy U as a function of the inter-atomic distance r. Which diagram corresponds to stable molecules found in nature.

The relationship between the force F and the position x of a body is as shown in the figure. The work done in displacing the body from x = 1 m to x = 5 m will be:

A particle is placed at the origin and a force F = kx is acting on it (where k is positive constant). If U(0) = 0, the graph of U(x) versus x will be (where U is the potential energy function) 

A body of mass 1 kg begins to move under the action of a time dependent force $F=\left(2t \hat{i}+3t^2 \hat{j}\right)$ N, where $\hat{i}$ and $\hat{j}$ are unit vectors along X and Y axis, What power will be developed by the force at the time (t) ?

(a) $\left(2t^2+4t^4\right)W$         

(b) $\left(2t^3+3t^4\right)W$

(c) $\left(2t^3+3t^5\right)W$         

(d) $\left(2t+3t^3\right)W$

What is the minimum velocity with which a body of mass m must enter a vertical loop of radius R so that it can complete the loop?
 

A block of mass 10 kg, moving in the x-direction with a constant speed of 10 ms^-1, is subjected to a retarding force \(F=0.1x\) J/m during its travel from x=20m to 30m. Its final KE will be :