Relation between Work Done and PE

Q.

A stone projected vertically upwards from the ground reaches a maximum height h. When it is at a height $\frac{3h}{4}$, the ratio of its kinetic and potential energies is

1. 1 : 3

2. 3 : 4

3. 4 : 3

4. 3 : 1

Q. the potential energy of a particle of mass 100g moving along x axis is given by U=5x(x-4), where x in metre find period of oscillation

Q. why is it that the frequency of oscillation of potential energy and kinetic energy is twice as that of displacement or velocity or acceleration of a partocle excecuting shm

Q. Potential energy of a particle of mass 2 kg oscillating on x axis is given as U=(x-2)^2-10.The total energy of oscillation is 26 J.Find the maximum speed of particle

Q. The Potential energy of a particle of mass 100g along x-axis is given by U = 5x(x - 4), where x is in metre. The Period of oscillation is

Q. A particle is in simple harmonic motion with amplitude a.when its displacement from mean psition is a/2, which of following will not be one half of its maximum value (a)acceleration (b)_velocity (c)potential energy (d)both 2 and 3

Q. A particle of mass m is located in a unidimensional potential field where potential energy of the particle depends on the coordinate x as U(x) = A/x^2 - B/x where A and B are positive cons†an ts. Find the time period of small oscillations that the particle perform about equilibrium position .

Q.

If only the conservative forces are acting on the body, then its total

1. Kinetic energy is conserved

2. Potential energy is conserved

3. Either potential or kinetic energy could be conserved

4. Mechanical energy is conserved

Q. The potential energy of a particle of mass 1 kgalong x-axis is U= 5(1- cos3x)J. The time periodof small oscillation is2т(2)3 5(1) 2T/53/5(3)2TTC(4)2/5

Q. the potential energy of a particle of mass 100g moving along x axis is given by U=5x(x-4) where x is in meter. the period of oscillation is ?

Q. A body of mass $5\text{kg}$ is dropped from a tower of height $10\text{m}$. Find the difference between work done $\text{(}J)$ by gravity and change in potential energy of the body from ${}^{\prime }{A}^{\prime }$ to ${}^{\prime }{B}^{\prime }$ (Take $g=10\frac{m}{s^2}$)

1. $-1000\text{joule}$
2. $-100\text{joule}$
3. $1000\text{joule}$
   
4. $2000\text{joule}$

Q. a spring is loaded with two blocks of masses m1 and m2, where m1 is rigidly fixed with the spring and m2 is just kept on the block m1.the maximum energy of oscillation is possible for the system having the block m2 in contact with m1 is (1)m1^2g^2/2k (2)m2^2g^2/2k (3)(m1+m2)^2g^2/2k (4)none of these

Q.

A given object takes n times as much time to slide down a 45° rough incline as it takes to slide down a perfectly smooth ${45}^o$ incline. The coefficient of kinetic friction between the object and the incline is given by

1. 

2. 

3. 

4. 

Q. a body of mass 2kg suspended through a vertical spring executes SHM of period 4 seconds if the oscillations are stopped and the body hangs in the equilibrium find the potential energy stored in the spring

Q. The potential energy of a particle of mass 250 gram moving along x axis is given by U=2x(x-3), where x is in metre. The frequency of oscillation is (in Hz) (1)8 pi (2)1/4 pi (3)4 pi (4)2/pi

Q. 79.The potential energy of a particle of mass 100g moving along x-axis is given by U=5(x-4), where x is in meter.The period of oscillation is 1)0.2s 2)0.1 s 3) s 4)1/ s

Q. 111.The time taken by a particle of mass 0.2gm executing S.H.M. to go from mean position to half of the amplitude is 0.2s. If the amplitude of oscillation is 2cm, then potential energy of the particle at x=1.2 cm. is, [x us the displacement from the mean position and potential energy is zero for x=0]

Q. Consider a rain drop of mass $1\text{g}$ falling from a height of $2\text{km}$. It hits the ground with a speed of $50\text{m/s}$. The work done by resistive force of air is
$(g=10{\text{m/s}}^2)$

1. $-187.5\text{J}$
2. $43.75\text{J}$
3. $-18.75\text{J}$
4. $14.375\text{J}$

Q. a particle executes simple harmonic motion with amplitude of a.when displacement from mean position is a/2 which of following will not be one half of its maximum value? (a)acceleration (b)velocity (c)potential energy (d)both 2 and

Q.

When work is done on a body by an external force, its

1. Only kinetic energy increases

2. Only potential energy increases

3. Both kinetic and potential energies may increase

4. Sum of kinetic and potential energies remains constant

Q. The potential energy of a particle of mass m is given by U(x) = U(1 - cosax), where U, and a are constant. Time period of small oscillation of the particle is

Q. A uniform chain of mass $m$ and length $L$ hangs on a table with two thirds of its length on the table. The work done by a person to put the hanging part back on the table will be

1. $\frac{mgL}{18}$
2. $\frac{mgL}{9}$
3. $\frac{mgL}{27}$
4. $mgL$

Q.

An angry bird (flightless) of mass 5 kg is projected with a speed of 25 m/s at an angle of ${37}^{\circ }$ with the horizontal. When it reaches its maximum height, it screams "fire in the hole!” and decides to take a massive 1 kg dump on Ram standing directly below it. What will be the magnitude of the horizontal velocity of the bird after release?

1. 20 m/s

2. 10 m/s

3. 25 m/s

4. None of these

Q. The potential energy of a particle in a certain field has the form $U=\frac{a}{r^2}-\frac{b}{r},$ where $a$ and $b$ are postive constants, $r$ is the distance from the centre of the field.

1. the value of $r_0$ corresponding to the equilibrium position of the particle is $\frac{a}{b}$
2. Particle is in unstable equiltibrium.
3. the minimum attractive force is $-\frac{b^2}{27a^3}$
4. the value of $r_0$ corresponding to the equilibrium position of the particle is $\frac{2a}{b}$

Q. 12.A particle of mass 4gis in a gravitational potential field given by V=(800x²+150)erg/g.Its frequency of oscillation is ---------

Q. the potential energy of a particle of mass 100g moving along x axis is given by U = 5x(x-4) ; where x is in metre .The period of oscillation is

Q. CONDITIONS FOR CONSERVATION OF MECHANICAL ENERGY OF A SYSTEM

Q. There are two massless springs A and B of spring constant $K_A$ and $K_B$ respectively and $K_A>K_B$. If $W_A$ and $W_B$ be denoted as work done on A and work done on B respectively, then

1. If they are compressed to same distance, $W_A>W_B$
2. If they are compressed by same force (upto equilibrium state) $W_A<W_B$
3. If they are compressed by same distance, $W_A<W_B$
4. If they are compressed by same force (upto equilibrium state) $W_A>W_B$

Q.

A spring of spring constant $5\times {10}^{3}N/m$is stretched initially by 5 cm from the unstretched position. Then the work required to stretch it further by another 5 cm is

1. 6.25 N-m

2. 12.50 N-m

3. 18.75 N-m

4. 25.00N-m

Q. The potential energy (in joules) of a particle of mass $1\text{kg}$ moving in a plane is given by $U=3x+4y$. The position coordinates of the point being $x$ and $y$, measured in metres. If the particle is at rest at $(6,4)$; then

1. its acceleration is of magnitude $5{\text{m/s}}^2$
2. its speed when it crosses the $y-$axis is $10\text{m/s}$
3. it crosses the $y-$ axis $(x=0)$ at $y=-4$
4. it moves in a straight line passing through the origin $(0,0)$