Two point masses 1 and 2 move with uniform velocities →v1 and →v2→v1 and →v2 respectively. Their initial position vectors are →r1 and →r2→r1 and →r2 respectively. Which of the following should be satisfied for the collision of the point masses ?
1. →r2-→r1|→r2+→r1|=→v2+→v1|→v2-→v1|→r2−→r1∣∣→r2+→r1∣∣=→v2+→v1∣∣→v2−→v1∣∣
2. →r2-→r1|→r2-→r1|=→v2-→v1|→v2-→v1|→r2−→r1∣∣→r2−→r1∣∣=→v2−→v1∣∣→v2−→v1∣∣
3. →r2-→r1|→r2+→r1|=→v2-→v1|→v2+→v1|→r2−→r1∣∣→r2+→r1∣∣=→v2−→v1∣∣→v2+→v1∣∣
4. →r2+→r1|→r2+→r1|=→v2-→v1|→v2+→v1|→r2+→r1∣∣→r2+→r1∣∣=→v2−→v1∣∣→v2+→v1∣∣
If length of string is l = 103m, TmaxTmin=4l = 103m, TmaxTmin=4
where = Maximum tension in the string
Tmin=Minimum tension in the string.Tmin=Minimum tension in the string.
Velocity at highest point is -Velocity at highest point is −
1. 10 m/s
2. 20 m/s
3. 10√2m/s10√2m/s
4. 10√3 m/s10√3 m/s
A mass m moving horizontally (along the x-axis) with velocity v collides and sticks to mass of 3m moving vertically upward (along the y-axis) with velocity 2v. The final velocity of the combination is
(a) 14vˆi+32vˆj
(b) 13vˆi+23vˆj
(c) 23vˆi+13vˆj
(d) 32vˆi+14vˆj
If a body of mass m moving with velocity u collides head-on elastically with another identical body at rest. After collision , velocity of the second body will be
(1) zero
(2) u
(3) 2u
(4) data insufficient
A sphere of mass m moving horizontally with velocity v0 collides against a pendulum bob of mass m. If the two masses stick together after the collision, then the maximum height attained is
(1) v202g
(2) v204g
(3) v206g
(4) v208g
A ball of mass m moving with a speed u undergoes a head-on elastic collision with a ball of mass nm initially at rest. The fraction of initial energy transferred to the heavier ball is
(1) n1+n
(2) n(1+n)2
(3) 2n(1+n)2
(4) 4n(1+n)2
A body of mass m1 moving with uniform velocity of 40 m/s collides with another mass m2 at rest and then the two together begin to move with uniform velocity of 30 m/s. The ratio of their masses m1m2 is
(1) 0.75
(2) 1.33
(3) 3.0
(4) 4.0
K is the force constant of a spring. The work done in increasing its extension from l1 to l2 will be
(1) K(l2-l1)
(2) K2(l2+l1)
(3) K(l22-l21)
(4) K2(l22-l21)
The points of maximum and minimum attraction in the curve between potential energy (U) and distance (r) of a diatomic molecules are respectively -
(a) Sand R
(b) T and S
(c) R and S
(d) S and T
A body of mass 1 kg is thrown upwards with a velocity of 20 ms-1. It momentarily comes to rest after attaining a height of 18 m. How much energy is lost due to air friction? (g=10) ms-2
1. 20 J
2. 30 J
3. 40 J
4. 10 J