A rough vertical board has an acceleration ‘a’ so that a 2 kg block pressing against it does not fall. The coefficient of friction between the block and the board should be

(1) > g/a

(2) < g/a

(3) = g/a

(4) > a/g

It is easier to draw up a wooden block along an smooth inclined plane than to haul it vertically, principally because 

(1) The friction is reduced

(2) The mass becomes smaller

(3) Only a part of the weight has to be overcome

(4) ‘g’ becomes smaller

A mass of 100g strikes the wall with speed 5m/s at an angle as shown in figure and it rebounds with the same speed. If the contact time is $2\times {10}^{-3}\sec$, what is the force applied on the mass by the wall 

(1) $250\sqrt{3}$N to right

(2) 250 N to right

(3) $250\sqrt{3}$N to left

(4) 250 N to left

A lead ball strikes a wall and falls down, a tennis ball having the same mass and velocity strikes the wall and bounces back. Check the correct statement

(1) The momentum of the lead ball is greater than that of the tennis ball

(2) The lead ball suffers a greater change in momentum compared with the tennis ball

(3) The tennis ball suffers a greater change in momentum as compared with the lead ball

(4) Both suffer an equal change in momentum

A ball of weight 0.1 kg coming with speed 30 m/s strikes with a bat and returns in opposite direction with speed 40 m/s, then the impulse is (Taking final velocity as positive) 

(1) $-0.1\times \left(40\right)-0.1\times \left(30\right)$

(2) $0.1\times \left(40\right)-0.1\times (-30)$

(3) $0.1\times \left(40\right)+0.1\times (-30)$

(4) $0.1\times \left(40\right)-0.1\times \left(20\right)$

A ball of mass m falls vertically to the ground from a height h₁ and rebound to a height h₂. The change in momentum of the ball on striking the ground is 

(1) $mg(h_1-h_2)$

(2) $m\left(\sqrt{2g{h}_1}+\sqrt{2g{h}_2}\right)$

(3) $m\sqrt{2g(h_1+h_2)}$

(4) $m\sqrt{2g}(h_1+h_2)$

Consider the following two statements

1. Linear momentum of a system of particles is zero

2. Kinetic energy of a system of particles is zero Then 

(1) 1 implies 2 and 2 implies 1

(2) 1 does not imply 2 and 2 does not imply 1

(3) 1 implies 2 but 2 does not imply 1

(4) 1 does not imply 2 but 2 implies 1

A force-time graph for a linear motion is shown in figure where the segments are circular. The linear momentum gained between zero and 8 second is 

1. $-2\pi newton\times second$

2. $Zeronewton\times second$

3. $+4\pi newton\times second$

4. $-6\pi newton\times second$

A particle of mass m moving with a velocity u makes an elastic one dimensional collision with a stationary particle of mass m establishing a contact with it for extremely small time T. Their force of contact increases from zero to F₀ linearly in time $\frac{T}{4}$, remains constant for a further time $\frac{T}{2}$ and decreases linearly from F₀ to zero in further time $\frac{T}{4}$ as shown. The magnitude possessed by F₀ is

(1) $\frac{mu}{T}$

(2) $\frac{2mu}{T}$

(2) $\frac{4mu}{3T}$

(4) $\frac{3mu}{4T}$

A body of weight 50 N placed on a horizontal surface is just moved by a force of 28.2 N. The frictional force and the normal reaction are

(1) 10 N, 15 N

(2) 20 N, 30 N

(3) 2 N, 3 N

(4) 5 N, 6 N