Work, Energy and Power

The speed of the block when it reaches the point $Q$ is

A block of mass 0.18 kg is attached to a spring of force-constant 2 N/m. The coefficient of friction between the block and the floor is 0.1. Initially the block is at rest and the spring is un-stretched. An impulse is given to the block as shown in the figure. The block slides a distance of 0.06 m and comes to rest for the first time. The initial velocity of the block in m/s is $V=N/10$. Then $N$ is

If the total energy of the particle is E, it will perform periodic motion only if

The acceleration of this particle for $|x|>X_0$ is

A block of mass 2 kg is free to move along the $x$-axis. It is at rest and from $t=0$ onwards it is subjected to a time-dependent force $F(t)$ in the $x$ direction. The force $F(t)$ varies with $t$ as shown in the figure. The kinetic energy of the block after 4.5 seconds is

Column II shows five systems in which two objects are labelled as X and Y. Also in each case a point P is shown. Column I gives some statements about X and/or Y. Match these statements to the appropriate system(s) from Column II.

A light inextensible string that goes over a smooth fixed pulley as shown in the figure connects two blocks of masses 0.36 kg and 0.72 kg. Taking $g=10\ \mathrm{m/s^2}$, find the work done (in joules) by the string on the block of mass 0.36 kg during the first second after the system is released from rest.

The speed of the block at point B immediately after it strikes the second incline is

The speed of the block at point C, immediately before it leaves the second incline is

A block (B) is attached to two unstretched springs S1 and S2 with spring constants $k$ and $4k$, respectively (see figure I). The other ends are attached to identical supports M1 and M2 not attached to the walls. The springs and supports have negligible mass. There is no friction anywhere. The block B is displaced towards wall 1 by a small distance $x$ (figure II) and released. The block returns and moves a maximum distance $y$ towards wall 2. Displacements $x$ and $y$ are measured with respect to the equilibrium position of the block B. The ratio $\frac yx$ is

A bob of mass M is suspended by a massless string of length L. The horizontal velocity V at position A is just sufficient to make it reach the point B. The angle $\theta$ at which the speed of the bob is half of that at A, satisfies

STATEMENT-1: A block of mass $m$ starts moving on a rough horizontal surface with a velocity $v$. It stops due to friction between the block and the surface after moving through a certain distance. The surface is now tilted to an angle of 30° with the horizontal and the same block is made to go up on the surface with the same initial velocity $v$. The decrease in the mechanical energy in the second situation is smaller than that in the first situation.

because

STATEMENT-2: The coefficient of friction between the block and the surface decreases with the increase in the angle of inclination.

The ratio $x_1/x_2$ is

A small object of uniform density rolls up a curved surface with an initial velocity $v$. It reaches up to a maximum height of $\dfrac{3v^2}{4g}$ with respect to the initial position. The object is