urgent!!! these are ques. from CH3 ,CH4 and CH5 .

1) 2 balls of diff. mass are thrown up with same u . max. height attained by them are h1 and h2. what is h1/h2 ??

2) give magnitude and direction of the net force of the rain drop falling with a constant speed.

3)what is the angle between velocity and acc. at the highest point of the projectile motion?

4)what is the work done by the centripetal force on a object revolving in a circular path.

5) 2 vectors 5i +7j -3k and 2i +2j - ak are mutually perpendicular . find the value of 'a'.

6)A spring balance is attached to the ceiling of a lift. A man hangs his bag on the spring & the spring reads 49N when the lift is stationary. What will be the reading on the balance if the lift starts moving down with an acceleration 5metre per second square.

7. The ceiling of a hall is 20metre high what is the maximum horizontal distance that the ball thrown with a speed 40 m / s can go without hitting the ceiling of a hall ? (G=10 m/s square)

8. The equation of trajectory of an oblique project tile is Y= (root 3 ) x - gx2 / 2 . What are the initial velocity & the angle porjection of the projectile?

9. Show that there are two angles of projection for which the horizontal range is same . Prove that the sum of maximum heights of these two angles does not depend upon the angle of projection.


10. The shell of mass 0.020kg is fired from a gun of mass 100kg. If the muzzle speed of the shell is 80 metre per second, what is the recoil velocity of the gun?


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(1) Maximum height reached is independent of the mass of the body and depends only on on velocity (u). Hence, the required ratio will be 1.

(3) At the highest point the particle only has horizontal velocity. Also acceleration(in this case g) is acting vertically downwards. Hence, the required angle is 90 degrees.

(4) Work done by centripetal force on an object revolving around the circular path is zero because the net displacement is zero.

(5) Two vectors are mutually perpendicular. This means that the dot product of two vectors will be zero.

Dot product of two vectors 5i + 7j - 3k and 2i + 2j - ak will be (5 x 2) + (7 x 2) + 3a

For this to be equal to zero, a should be equal to - 8.

(10) m = 0.002 kg, M = 100 kg and v = 80 m/s

Therefore, the recoil velocity of the gun  = - (0.002 x 80)/100 = - 0.0016 m/s

(9) 

Horizontal Range is given by:

 

Sum of maximum heights will be:

 

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