The 'e' Equation

Q. A hollow sphere of mass m and radius r is rolling without slipping on a horizontal surface so that its centre of mass has speed v .the work done required to stop the hollow sphere will be

Q. find the relative error in Z , if Z=A^4B^{1/3}/CD^{3/2}AND THE percentage error in the measurement of A, B, CandD are 4%, 2%, 3%, 1%

Q.

The relationship between force and position is shown in the figure given (in one dimensional case). The work done by the force in displacing a body from x = 1 cm to x = 5 cm is

1. 60 ergs

2. 70 ergs

3. 20 ergs

4. 700 ergs

Q. a particle of mass 2kg , executing SHM has amplitude 20cm and time period 1s .the max speed i

Q.

A spring is stretched by 0.20 m, when a mass of 0.50 kg is suspended. When a mass of 0.25 kg is suspended, then its period of oscillation will be ( g = 10 m/$s^2$ )

1. 0.628 sec

2. 0.137 sec

3. 1.00 sec

4. 0.328 sec

Q.

In case of a projectile, the angular momentum is minimum

1. at the starting point

2. on return to the ground

3. at some location other than those mentioned above

4. at the highest point

Q. 59. A boat of mass 90kg is floating in still water. A boy of mass 30kg walks from the stern to bow. The length of the boat is 3m. Calculate the distance through which the boat will move.

Q. A ball is thrown up vertically with a velocity of 20m/s, at what heigh t will its kinetic energy be halfits orginal volume?

Q.

When a ball is allowed to fall from a height of 20 m, 40% of its energy is lost due to impact. After one impact the ball will go up to a height of

1. 8 m

2. 15 m

3. 10 m

4. 12 m

Q. A man of mass 50 kg is moving up an inclined plane pull ablock of mass 25 kg with constant speed 1 m/s. Frictioncoefficient between block and plane is 0.5. Assuming thatman doesnt slips. Power delivered by man

Q. ball of mass 100 kg is thrown upward it Rises to a maximum height of 100m at what height its kinetic energy will reduce to 60%

Q. A ball is thrown vertically downwards from a heigh tof 20m with ani nitial velocity v^2.It collides witht h eground, loses 50% of its energy in thec ollision and rebounds to the same height.The initial velocity v is?\lbrack g=10m/s^2\rbrack

Q. 16.A block of mass 0.05 kg when placed on a rough 15 degree inclined plane slides down without acceleration . The inclination is then increased to 30 degree.what would be the acceleration of the block. Solve it by diagram.

Q. 76.)A hollow sphere is released from the top of an inclinedplane of inclination 0. (a) What should be the minimumcoefficient of friction between the sphere and the planeto prevent sliding ? (b) Find the kinetic energy of theball as it moves down a length l on the incline if thefriction coefficient is half the value calculated in part (a).

Q. A particle is projected with a velocity v such that its range on the horizontal plane is twice the greatest height
attained by it. The range of the projectile is (where is acceleration due to gravity)

1. 
2. 
3. 
4. 

Q. 123.Two cars A and B are approaching in opposite directions with speeds 10 metre per sec and 20 metreper sec respectively when their seperations is d then A and B start deccelerating at 4 metrepersecsquare and 5metreper secsquare rwspectively.minimum value of d to avoid collision is

Q.

Two blocks of the masses 10 kg and 4 kg are connected by a spring of negligible mass and placed on a frictionless horizontal surface. An impulse gives a velocity of 14 m/s to the heavier block. The velocity of centre of mass is

1. 20 m/s

2. 5 m/s

3. 10 m/s

4. 30 m/s

Q.

5 particles are moving along the x-axis with different velocities. Match their velocity time graphs with corresponding acceleration time graph.

1. p - iv, q - ii, r - i, s - iii, t - v
2. p - v, q - ii, r - i, s - iv, t - iii
3. p - iv, q - ii, r - i, s - iii, t - i
4. p - i, q - v, r - i, s - iii, t - iv

Q. For a perfectly elastic collision, the value of coefficient of restitution is

1. equal to 0
2. less than 1
3. equal to 1
4. less than or equal to 1

Q. Calculate the rate of flow of glycerine of density {1.20×10^3kg/m^3 through the conical section of a { pipe. If the radii ends 0.1m and 0.02m and the { pressure drop across the length is 120N/m^2

Q.

If a stone is thrown with a speed $v_0$ at an angle ${\theta }_0$ with horizontal, find the velocity of the stone when its line of motion makes an angle $\theta$ with horizontal.

1. 

2. 

3. 

4. 

Q. A block $A$ of mass $2\text{kg}$ moving with speed of $15\text{m/s}$, collides with a stationary block $B$ of mass $5\text{kg}$. If the coefficient of restitution is $0.6$, find the magnitude of velocity of blocks $A$ and $B$ after the collision respectively.

1. $5.2\text{m/s}$ and $10.5\text{m/s}$
2. $3.5\text{m/s}$ and $6.85\text{m/s}$
3. $10.5\text{m/s}$ and $5.2\text{m/s}$
4. $2.15\text{m/s}$ and $6.85\text{m/s}$

Q. A smooth sphere of mass $m$ is moving on a horizontal plane with velocity $3\hat{i}+\hat{j}$. It collides with a vertical wall which is parallel to vector$\hat{j}$. If the coefficient of restitution is $0.5$, the angle of velocity of the ball with repect to the normal to the wall after impact will be

1. ${30}^o$
2. ${\tan }^{-1}(\frac{1}{3})$
3. ${\cos }^{-1}\left(\frac{2}{\sqrt{13}}\right)$
4. ${\sin }^{-1}\left(\frac{2}{\sqrt{13}}\right)$

Q. A ball falls on the ground from a height of 2.0 m and rebounds up to a height of 1.5 m. Find the coefficient of restitution.

Q.

In case of streamlined flow of liquid, the loss of energy is

1. minimum

2. infinite

3. zero

4. maximum

Q. 30. Consider a system consisting of two equal masses tied by massless string placed over a wedge such that string passes over a frictionless pulley then determine acceleration of centre of mass

Q.

A metal ball falls from a height of 32 m on a steel plate. If the coefficient of restitution is 0.5, to what height will the ball rise after the second bounce

1. 2 m

2. 4 m

3. 8 m

4. 16 m

Q. The velocity of point R of the rod just after impact with the bumper is (in m/s)

1. $1.2\sqrt{5}$
2. $1.2$
3. $1.2\sqrt{5(2+\sqrt{3})}$
4. $1.2\sqrt{5(2-\sqrt{3})}$

Q. The ab of length l and mass m can rotate freely about A in a vertical plane. a point mass m is attached to the other end of the rod and the system is released form its horizontal position . the initial angular acceleration is ?

Q.

A ball collides directly with another ball at rest and is itself brought to rest by the impact. If one fourth of initial kinetic energy is destroyed in the collision, the coefficient of restitution of the collision is

1. $\frac{1}{2}$

2. $\frac{1}{4}$

3. $\frac{3}{4}$

4. $\frac{1}{3}$