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Work, Power & Energy

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IIT-JEE 2011 Q51 Advance 8. ARCHIVE: JEE ADVANCED Numerical
A block of mass 0.18 kg is attached to a spring of force constant $2 \, Nm^{-1}$ . 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 $ms^{-1}$ is $V = \frac{N}{10}$ . Find the value of N.
2010 Q52 Advance 7. ARCHIVE: JEE MAIN MCQ
The potential energy function for the force between two atoms in a diatomic molecule is approximately given by $U(x) = \frac{a}{x^{12}} - \frac{b}{x^6}$ , where $a$ and b are constant and x is the distance between the atoms. If the dissociation energy of the molecule is $D=\left[U(x=\infty)-U_{\text{atequilibrium}}\right]$ , D is
A.
$\frac{b^{2}}{6a}$
B.
$\frac{b^{2}}{2a}$
C.
$\frac{b^{2}}{12a}$
D.
$\frac{b^{2}}{4a}$
IIT-JEE 2010 Q53 Advance 8. ARCHIVE: JEE ADVANCED MCQ
A block of mass $2\mathrm{kg}$ 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 $4.5\mathrm{s}$ is
A.
4.50 J
B.
7.50 J
C.
5.06 J
D.
14.06 J
IIT-JEE 2008 Q54 Advance 8. ARCHIVE: JEE ADVANCED MCQ
A block (B) is attached to two unstretched springs $S_{1}$ and $S_{2}$ with spring constants k and 4k, respectively. The other ends are attached to two supports $M_{1}$ and $M_{2}$ 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 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.
4
B.
2
C.
$\frac{1}{2}$
D.
$\frac{1}{4}$
IIT-JEE 2008 Q55 Advance 8. ARCHIVE: JEE ADVANCED MCQ
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
A.
$\theta = \frac {\pi}{4}$
B.
$\frac{\pi}{4} < \theta < \frac{\pi}{2}$
C.
$\frac{\pi}{2}<\theta<\frac{3\pi}{4}$
D.
$\frac{3\pi}{4} < \theta < \pi$
IIT-JEE 2007 Q56 Advance 8. ARCHIVE: JEE ADVANCED MCQ
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.
A.
If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.
B.
If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.
C.
If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.
D.
If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.
IIT-JEE 2004 Q57 Advance 8. ARCHIVE: JEE ADVANCED MCQ
A particle is placed at the origin and a force $F = kx$ is acting on it (where $k$ is a positive constant). If $U(0) = 0$ , the graph of $U(x)$ versus $x$ will be: (where $U$ is the potential energy function)
A.
B.
C.
D.
IIT-JEE 2003 Q58 Advance 8. ARCHIVE: JEE ADVANCED MCQ
If $W_{1}$ , $W_{2}$ and $W_{3}$ represent the work done in moving a particle from A to B along three different paths 1, 2 and 3 respectively (as shown) in the gravitational field of a point mass m. Find the correct relation between $W_{1}$ , $W_{2}$ and $W_{3}$
A.
$W_{1} > W_{2} > W_{3}$
B.
$W_{1}=W_{2}=W_{3}$
C.
$W_{1} < W_{2} < W_{3}$
D.
$W_{2} > W_{1} > W_{3}$
IIT-JEE 2002 Q59 Advance 8. ARCHIVE: JEE ADVANCED MCQ
A particle, which is constrained to move along x-axis, is subjected to a force in the same direction which varies with the distance x of the particle from the origin as $F(x) = -kx + ax^{3}$ . Here, k and a are positive constant. For $x \geq 0$ , the functional form of the potential energy $U(x)$ of the particle is
A.
B.
C.
$U(x)$
D.
$U(x)$
2000 Q60 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A dam is situated at a height of 550 metre above sea level and supplies water to a power house which is at a height of 50 metre above sea level. 2000 kg of water passes through the turbines per second. The maximum electrical power output of the power house if the whole system were 80% efficient is
A.
8 MW
B.
10 MW
C.
12.5 MW
D.
16 MW
IIT-JEE 2000 Q61 Advance 8. ARCHIVE: JEE ADVANCED MCQ
A wind-powered generator converts wind energy into electrical energy. Assume that the generator converts a fixed fraction of wind energy interception by its blades into electrical energy. For wind speed v, the electrical power output will be proportional to
A.
$v$
B.
$v^{2}$
C.
$v^{3}$
D.
$v^{4}$
IIT-JEE 1999 Q62 Advance 8. ARCHIVE: JEE ADVANCED MCQ
A spring of force constant k is cut into two pieces such that one piece is double the length of the other. Then the long piece will have a force constant of
A.
$\left(\frac{2}{3}\right)k$
B.
$\left(\frac{3}{2}\right)k$
C.
3k
D.
6k
IIT-JEE 1998 Q63 Advance 8. ARCHIVE: JEE ADVANCED MCQ
A stone tied to a string of length L is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at the lowest position and has a speed u. The magnitude of the change in velocity as it reaches a position where the string is horizontal is
A.
$\sqrt{u^{2}-2gL}$
B.
$\sqrt{2gL}$
C.
$\sqrt{u^{2}-gL}$
D.
$\sqrt{2(u^{2}-gL)}$
IIT-JEE 1998 Q64 Advance 8. ARCHIVE: JEE ADVANCED MCQ
A force $\vec{F} = -k(y\hat{i} + x\hat{j})$ , where $k$ is a positive constant, acts on a particle moving in the $xy$ plane. Starting from the origin, the particle is taken along the positive $x$ -axis to the point $(a,0)$ , and then parallel to the $y$ -axis to the point $(a,a)$ . The total work done by the force on the particle is
A.
$-2ka^{2}$
B.
$2ka^{2}$
C.
$-ka^{2}$
D.
$ka^{2}$
IIT-JEE 1994 Q65 Advance 8. ARCHIVE: JEE ADVANCED MCQ
A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration $a_{c}$ is varying with time t as $a_{c}=k^{2}rt^{2}$ , where k is a constant. The power delivered to the particle by the force acting on it is
A.
$2\pi mk^{2}r^{2}$
B.
$mk^{2}r^{2}t$
C.
$\frac{(mk^{4}r^{2}t^{5})}{3}$
D.
Zero
IIT-JEE 1987 Q66 Advance 8. ARCHIVE: JEE ADVANCED MSQ
A particle is acted upon by a force of constant magnitude which is always directed perpendicular to the velocity of the particle. The motion of the particle takes place in a plane. From the information given, conclude that the particle
A.
has constant velocity.
B.
has constant acceleration.
C.
has constant kinetic energy.
D.
moves in a circular path.
IIT-JEE 1985 Q67 Advance 8. ARCHIVE: JEE ADVANCED MCQ
A uniform chain of length L and mass M is lying on a smooth table and one-third of its length is hanging vertically down over the edge of the table. The work required to pull the hanging part on the table is
A.
MgL
B.
$\frac{MgL}{3}$
C.
$\frac{MgL}{9}$
D.
$\frac{MgL}{18}$
IIT-JEE 1984 Q68 Advance 8. ARCHIVE: JEE ADVANCED MCQ
A body is moved along a straight line by a machine delivering constant power. The distance moved by the body in time t is proportional to
A.
$t^{\frac{1}{2}}$
B.
$t^{\frac{3}{4}}$
C.
$t^{\frac{3}{2}}$
D.
$t^{2}$
IIT-JEE 1980 Q69 Advance 8. ARCHIVE: JEE ADVANCED MCQ
Two masses of 1 g and 4 g are moving with equal kinetic energies. The ratio of the magnitudes of their momenta is
A.
4:1
B.
$\sqrt{2}$ :1
C.
1:2
D.
1:16
IIT-JEE 1980 Q70 Advance 8. ARCHIVE: JEE ADVANCED MCQ
If a machine is lubricated with oil,
A.
the mechanical advantage of the machine increases
B.
the mechanical efficiency of the machine increases
C.
both its mechanical advantage and efficiency increases
D.
its efficiency increases, but its mechanical advantage decreases
1960 Q71 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A 2 kg block is dropped from a height of 0.4 m on a spring of force constant $k = 1960 \, Nm^{-1}$ . The maximum compression of the spring is
A.
0.1 m
B.
0.2 m
C.
0.3 m
D.
0.4 m
1960 Q72 Advance 6. INTEGER/NUMERICAL ANSWER TYPE QUESTIONS Numerical
Two blocks A and B are connected to each other by a string and a spring. The string passes over a frictionless pulley as shown in figure. Block B slides over the horizontal top surface of a stationary block C and the block A slides along the vertical side of C, both with the same uniform speed. The coefficient of friction between the surfaces of the blocks is 0.2. The force constant of the spring is $1960 \, Nm^{-1}$ . If the mass of block A is 2 kg, calculate the mass of block B, in kg, and the energy stored in the spring in mJ. Take $g = 9.8 \, ms^{-2}$ .
Q73 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
Two equal masses are attached to the two ends of a spring of force constant $k$ . The masses are pulled out symmetrically to stretch the spring by a length $2x_0$ over its natural length. The work done by the spring on each mass.
A.
$kx_0^2$
B.
$-\frac{1}{2}kx_0^2$
C.
$2kx_0^2$
D.
$-kx_0^2$
Q74 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
An ideal spring is hung vertically from the ceiling. Spring extends by 6 cm from its natural length when 2 kg mass is attached to it. A downward external force is now applied to the mass to extend the spring slowly by an additional 10 cm. Work done by the external force is
A.
-1.2 J
B.
-1.8 J
C.
2.4 J
D.
1.6 J
Q75 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A crate of mass m falls from a height h onto the end of a platform, as shown in the figure. The spring is initially unstretched and the mass of the platform can be neglected. Assuming that there is no loss of energy, the maximum elongation of the spring is
A.
$\frac{mg+\sqrt{m^{2}g^{2}+2mghk}}{k}$
B.
$\frac{mg-\sqrt{m^{2}g^{2}+2mghk}}{k}$
C.
$\frac{k}{\sqrt{m^{2}g^{2}+2mghk}}$
D.
$\frac{\sqrt{m^{2}g^{2}+2mghk}}{k}$