34 . A strip of wood of length l is placed on a smooth horizontal surface . An insect starts from one end of the strip , walks with a constant velocity and reaches the other end in time t1 . it then flies off vertically . The strip moves a further distance l in time t2.
a>t2=t1 b>t2<t1 c>t2>t1
d>either b or c depending on the masses of the insect or the strip .
55 . A particle moves along the x-axis as follows : it starts from rest at t=0 from a point x=0 and comes to rest at t=1 at point x=1 . No other information is available about its motion for the intermediate time (0<t<1) . If α denotes the instanttaneous accleartion of the particle then
a> α cannot remain positive for t in the interval 0≤t≤1 .
b> mod α cannot exceed 2 at any point in its path .
c> mod α must be ≥ 4 at some point or points in the path
d> α must change sign during the motion , but no other assertion can be made with the information given
61. Two particles A and B start simultaneously from the same point and move in a horizontal plane . A has innial velocity u1 due east and acceleartion a1 due north . B has innitial velocity u2 due north and acceleration a2 due east .
a> Thier path must intersect
b> They must collide at some point
c> They will collide only if u1a1=a2u2
d> If u1>u2 and a1>a2 , the particles will have the same speed at some point of time
1ei 55 ta ke nie naa amar bhalo mato doubt achhe...
eta kono ekbar iit te esechhilo ...
1at any point of time 't',
x1 = u1 t , y1= 1/2a1t2
y2= u2 t , x2= 1/2 a2 t2
now if they collide, at that time 't', then,
x1=x2 => t=2 u1/ a2
also, y1=y2 => t= 2u2/ a1
both time are same.. so u1/a2= u2/a1 => a1u1 = a2u2.
now, velocities at any point of time:
V1 = √u12 + (a1t)2
v2 = √u2 2 +(a2t)2
if If u1>u2 and a1>a2 , then v1=v2 at some point of time..
finally option A is obvious! think abt the trajectory...
10655. a,b it cant be d because we can make other assertions from the given information....
134.) let mass of cheeti =m and vel of cheeti : v
again let mass of wood = M
then, no extrenal force, so conservation of mom..
so, vel of lakdi : mv/(m+M) = v' (say) obviously < v
now, t1 = L/v
and t2 = L/v'
v'< v => t2>t1
