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

An elevator and its load have a total mass of 800 kg .Find the tension in the supporting cable when the elevator, moving downward at 10 m/s is brought to rest with constant acceleration in a distance of 25 m. ( Take g = 10m/s² ) :-

(1) 6400 N

(2) 8000 N

(3) 9600 N

(4) Zero

Two blocks A and B of masses 3m and m respectively are connected by a massless and inextensible string. The whole system is is suspended by a massless spring as shown in figure. the magnitudes of acceleration of A and B immediately after the string is cut, are respectively

1. g, g/3

2. g/3, g

3. g, g

4. g/3, g/3

A car is negociating a curved road of radius R. The road is banked at angle $\mathrm{\theta }$. The coefficient of friction between the car and the road is ${\mu }_s$. The maximum safe velocity on this road is 

(a)$\sqrt{gR\left(\frac{\tan \theta +\mu s}{1-{\mu }_s\tan \theta }\right)}$ 

(b) $\sqrt{\frac{g}{R}\left(\frac{\tan \theta +\mu s}{1-{\mu }_s\tan \theta }\right)}$

(c) $\sqrt{\frac{g}{R^2}\left(\frac{\tan \theta +\mu s}{1-{\mu }_s\tan \theta }\right)}$

(d) $\sqrt{g{R}^2\left(\frac{\tan \theta +\mu s}{1-{\mu }_s\tan \theta }\right)}$

The length of a spring is l₁ and l₂, when stretched with a force of 4 N and 5 N respectively. Its natural length is

1. l₂ + l₁

2. 2(l₂-l₁)

3. 5l₁ - 4l₂

4. 5l₂ - 4l₁

Two stones of masses \(m\) and \(2m\) are whirled in horizontal circles, the heavier one in a radius \(\frac{r}{2}\) and the lighter one in the radius \(r.\) The tangential speed of lighter stone is \(n\) times that of heavier stone when they experience the same centripetal forces. The value of \(n\) is:

One end of the string of length \(l\) is connected to a particle of mass \(m\) and the other end is connected to a small peg on a smooth horizontal table. If the particle moves in a circle with speed \(v\), the net force on the particle (directed towards the centre) will be: (\(T\) represents the tension in the string)

A spring of force constant k is cut into lengths of ratio 1:2:3. They are connected in series and the new force constant is $k^{\text{'}}$. If they are connected in parallel and force constant is $k^{\text{'}\text{'}}, then k^{\text{'}}:k^{\text{'}\text{'}}$ is 

(1) 1:6

(2) 1:9

(3) 1:11

(4) 6:11