Law of Conservation of Mechanical Energy

Q.

What minimum horizontal speed should be given to the bob of a simple pendulum of length l so that it describes a complete circle?

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Q.

A block weighing 10 N travels down a smooth curved track AB joined to a rough horizontal surface (figure). The rough surface has a friction coefficient of 0.20 with the block. If the block starts slipping on the track from a point 1.0 m above the horizontal surface, how far will it move on the rough surface?

1. 0 m

2. 10 m

3. 20 m

4. 5 m

Q. 6. Each of the two strings of length 51.6cm and 49.1cm are tensions separately by 20N force. Mass per unit length of both strings is same and equal to 1g/m .when both Strings vibrate simultaneously the number of beats is

Q. 128.What is the minimum velocity with which a body of mass m must enter a vertical loop of radious R so that it can complete the loop.

Q.

A body of mass $1kg$ is thrown upwards with a velocity $20m{s}^{-1}$. It momentarily comes to rest after attaining a height of $18m$. How much energy is lost due to air friction ($g=10m{s}^{-2}$)

1. $20J$

2. $30J$

3. $40J$

4. $10J$

Q. a projectile is thrown with velocity v at an angle theta with horizontal. when the projectile is at a height equal to half of the maximum height, the vertical component of the velocity of projectile i

Q.

The bob of a pendulum is released from a horizontal position. If the length of the pendulum is 1.5 m, what is the speed with which the bob arrives at the lowermost point, given that it dissipated 5% of its initial energy against air resistance?

Q.

A particle of mass m is attached to a light string of length l, the other end of which is fixed. Initially the string is kept horizontal and the particle is given an upward velocity v. The particle is just able to complete a circle.

1. The string becomes slack when the particle reaches its highest point

2. The velocity of the particle becomes zero at the highest point.

3. The kinetic energy of the ball in initial position was

4. The particle again passes through the initial position.

Q. 4.A block of mass M is attached to two springs of spring constants K1 and K2 as shown in figure. the block is displaced by x towards right and released. the velocity of block when it is at x/2 will be

Q.

Mass m shown in the figure is in equilibrium. If it is displaced further by x and released find its acceleration just after it is released. Take pulleys to be light & smooth and strings light.

1. none of these

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Q.

A man weighing $60kg$ lifts a body of $15kg$ to the top of a building $10m$ high in $3\mathrm{minutes}$. His efficiency is

1. $10\%$

2. $20\%$

3. $30\%$

4. $40\%$

Q.

The system shown in fig. is released from rest with mass 2 kg in contact with the ground. Pulley and spring are massless, and friction is absent everywhere. The speed of 5 kg block when 2 kg block leaves the contact with the ground is (force constant of the spring $k=40N{m}^{-1}andg=10m{s}^{-2}$ ).

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Q.

A block attached to a spring, pulled by a constant horizontal force, is kept on a smooth surface as shown in fig. Initially, the spring is in the natural length state. Then the maximum positive work that the applied force F can do is (given that string does not break)

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Q.

A particle of mass 'm' and charge 'q' is accelerated through a potential difference of 'V' volt. Its energy is

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Q.

Which of the following quantity remains constant during the uniform circular motion?

1. Angular velocity

2. Velocity

3. Speed

4. Angular acceleration

Q. if speed of an object revolving in a circular path is doubled and angular sperd is reduced to half of original value then centripetal acceleration ill become

Q. A body of mass $m$ dropped from a certain height strikes a light vertical fixed spring of stiffness $k$. The height of its fall before touching the spring if the maximum compression of the spring is equal to $\frac{3mg}{k}$ is

1. $\frac{3mg}{2k}$
2. $\frac{2mg}{k}$
3. $\frac{3mg}{4k}$
4. $\frac{mg}{4k}$

Q. a ring of radius 1mis under pure rolling on a horizontal surface with cons†an t angular speed of 5rad/s . the linear speed of a point on the horizontal diameter at any ins†an t of time with respect to point of contact with the ground is 1) 4 m/s 2) 5m/s 3) 5\surd2m/s 4)10m/

Q. 7.Two paper screen A and B are separated by distance 100m. A bullet penetrates A and B at points P and Q respectively, where Q is 10 cm below P.if bullet is travelling horizontally attime of hitting A , the velocity of bullet at A is nearl

Q. The potential energy of a $1\text{kg}$ particle free to move along the $x-$ axis is given by $V=(\frac{x^4}{4}-\frac{x^2}{2})\text{J}$
The total mechanical energy of the particle is $2\text{J}$. Then the maximum speed is

1. $\frac{3}{\sqrt{2}}\text{m/s}$
2. $\sqrt{2}\text{m/s}$
3. $\frac{1}{\sqrt{2}}\text{m/s}$
4. $2\text{m/s}$

Q. a projectile is thrown with an initial velocity (vxi +vyj)m/s . if the range of the projectile is double the naximum height , then vy/vx

Q.

A toy gun uses a spring of force constant K. Before being triggered in the upward direction, the spring is compressed by a distance x. If the mass of the shot is m, on being triggered, it will go up to a maximum height of

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Q. 30 A particle is projected with a velocityv = (3i-1+2k) m/s and a constant accelerationacting on the particle is ä (-6i+2j-4k) m/s.Then the path of projectile is(1) Straight line(2) Circle(3) Parabola(4) Ellipse

Q. A projectile moves from ground such that its horizontal displacement is y=Kt\{1-alphat \} where k and alpha are cons†an ts and t is time .Find total timeof flightT and max.height attained (Ymax.

Q. A small stone of mass 100g is rotated in a vertical circle of radius 40 cm. What is the minimum speed needed at the lowest point for looping the loop?Also find the tension in the string at this point.

Q.

A mass m slips along a smooth hemispherical surface of radius R starting from rest at the top as shown.

The velocity of the mass at the bottom of the surface is

1. $\sqrt{Rg}$

2. $\sqrt{2Rg}$

3. $2\sqrt{\pi Rg}$

4. $2\sqrt{\pi Rg}$

Q. 58. A tank containing water has an orifice 2 metres below the surface of water. if there is no wastage of energy. find the speed of discharge.

Q. Two masses 6 kg and 4 kg are connected by massless flexible and inextensible string passing over massless and frictionless pulley. The magnitude of acceleration of centre of mass is (g = 10 ms–2)

Q. 184. A ball of mass 50 g is thrown upwards. It rises to 9 a maximum height of 100 m. At what height its kinetic energy will be reduced to 70%? (1) 30 m (3) 60 m (2) 40 m (4) 70 m

Q.

If a planet revolves around the sun which of the following doesn't remain constant ?

1. Angular momentum

2. Angular momentum and Total energy

3. Linear speed

4. Total energy