Work Power & Energy · Physics · JEE Advanced
MCQ (More than One Correct Answer)
When the distance of the piston from closed end is L = L0, the particle speed is v = v0. The piston is moved inward at a very low speed V such that $$V < < {{dL} \over L}{v_0}$$, where dL is the infinitesimal displacement of the piston. Which of the following statement(s) is/are correct?
Which of the following options is /are true?
A thin ring of mass 2 kg and radius 0.5 m is rolling without on a horizontal plane with velocity 1 m/s. A small ball of mass 0.1 kg, moving with velocity 20 m/s in the opposite direction hits the ring at a height of 0.75 m and goes vertically up with velocity 10 m/s. Immediately after the collision,
A ball moves over a fixed track as shown in the figure. From $A$ to $B$, the ball rolls without slipping. Surface $B C$ is frictionless. $K_A, K_B$ and $K_c$ are kinetic energies of the ball at $A, B$ and C , respectively. Then
Numerical
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
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 m/s2, 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.
Three objects A, B and C are kept in a straight line on a frictionless horizontal surface. These have masses m, 2m and m, respectively. The object A moves towards B with a speed 9 m/s and makes an elastic collision with it. Thereafter, B makes completely inelastic collision with C. All motions occur on the same straight line. Find the final speed (in m/s) of the object C.
There is a rectangular plate of mass M kg of dimensions ( $a \times b$ ). The plate is held in horizontal position by striking $n$ small balls each of mass m per unit area per unit time. These are striking in the shaded half region of the plate. The balls are colliding elastically with velocity $v$. What is $v$ ?
It is given $n=100, \mathrm{M}=3 \mathrm{~kg}, m=0.01 \mathrm{~kg}$; $b=2 m ; a=1 \mathrm{~m} ; g=10 \mathrm{~m} / \mathrm{s}^2$MCQ (Single Correct Answer)
| LIST - I | LIST - II | ||
|---|---|---|---|
| P. | $$\overrightarrow r $$(t)=$$\alpha $$ $$t\,\widehat i + \beta t\widehat j$$ | 1. | $$\overrightarrow p $$ |
| Q. | $$\overrightarrow r \left( t \right) = \alpha \cos \,\omega t\,\widehat i + \beta \sin \omega t\,\widehat j$$ | 2. | $$\overrightarrow L $$ |
| R. | $$\overrightarrow r \left( t \right) = \alpha \left( {\cos \omega t\,\widehat i + \sin \omega t\widehat j} \right)$$ | 3. | K |
| S. | $$\overrightarrow r \left( t \right) = \alpha t\,\widehat i + {\beta \over 2}{t^2}\widehat j$$ | 4. | U |
| 5. | E | ||
A particle of unit mass is moving along the x-axis under the influence of a force and its total energy is conserved. Four possible forms of the potential energy of the particle are given in Column I (a and U0 are constants). Match the potential energies in Column I to the corresponding statement(s) in Column II:
The magnitude of the normal reaction that acts on the block at the point Q is
The speed of the block when it reaches the point Q 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 s 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 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 $$\frac{y}{x}$$ 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$$^\circ$$ 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.
Statement 2 :
The coefficient of friction between the block and the surface decreases with the increase in the angle of inclination.
