A solid sphere is set into motion on a rough horizontal surface with a linear speed v in the forward direction and an angular speed in the anticlockwise direction as shown in figure. Find the linear speed of the sphere when it stops rotating and ω =
Two blocks of masses m1 and m2 are connected by a spring of spring constant k. The block of mass m2 is given a sharp empulse so that it acquires a velocity v0 towards right. Find the maximum elongation that the spring will suffer.
v0
v0
v0
v0
A ball of mass m hits the floor with a speed v making an angle of incidence θ with the normal. The coefficient of restitution is e. The speed of reflected ball and the angle of reflection of the ball will be
v' = v, θ = θ'
v' = , θ = 2θ'
v' = 2v, θ = 2θ'
v' =
A particle slides on surface of a fixed smooth sphere starting from top most point. The angle rotated by the radius through the particle, when it leaves contact with the sphere, is
What is the radius of curvature of the parabola traced out by the projectile in the previous problem at a point where the particle velocity makes an angle θ/2 with the horizontal?
A.
Let v be the velocity at the point where it makes an θ/2 angle with the horizontal.
The horizontal component remains unchanged. So
From figure
Putting the value of v from Eq (i), we get
A block of mass 2 kg is pushed against a rough vertical wall with a force of 40 N, coefficient of static friction being 0.5. Another horizontal force of 15 N, is applied
on the block in a direction parallel to the wall. If the block will move, then its direction would be
15o with 15 N force
53o with 15 N force
45o with 15 N force
75o with 15N force
A block is kept on the floor of an elevator at rest. The elevator starts descending with an acceleration of 12 m/s2. Find the displacement of the block during the first 0.2 s after the start. (Take, g = 10 m/s2)
30 cm
zero
20 cm
25 cm
A monkey of mass 15 kg is climbing on a rope with one end fixed to the ceiling. If it wishes to go up with an acceleration 1 m/s, how much force should it apply to the rope if rope is 5 m long and the monkey starts from rest?
150 N
> 160 N
165 N
150 < T ≤ 160 N
A body weighing 8 g when placed in one pan and 18 g when placed on the other pan of a false balance. If the beam is horizontal when both the pans are empty, then the true weight of the body is
13 g
9 g
22 g
12 g
A rod PQ of length l is moving with ends remaining in contact with frictionless wall and floor. If at the instant, shown the velocity of end Q is 2 m/s towards negative direction of x. The speed of end P will be