NCERT Solutions For Class 9 Science Chapter 9 Force and Laws of Motion

\begin{array}{l}\text{Given, mass of the dumbell, m = 10 kg}\\ \text{ distance covered by the dumbell,}\\ \text{ s = 80 cm = 0}\text{.8 m }\\ {\text{acceleration in the downward direction, a = 10 ms}}^{\text{-2}}\\ \text{initial velocity of the dumbell, u = 0}\\ \text{final velocity of the dumbell, v = ?}\\ \text{On using the third equation of motion,}\\ {\text{ v}}^{\text{2}}{\text{ = u}}^{\text{2}}\text{+2as}\\ \text{On putting the given values,}\\ {\text{ v}}^{\text{2}}{\text{ = 0}}^{\text{2}}{\text{ + 2(10 ms}}^{\text{-2}}\text{)(0}\text{.8 m)}\\ {\text{ = 16 m}}^{\text{2}}{\text{s}}^{-2}\\ \text{or, v = }\sqrt{{\text{16 m}}^{\text{2}}{\text{s}}^{-2}}{\text{ = 4 ms}}^{\text{-1}}\\ \text{Therefore, the momentum with which the dumbell hits the}\\ {\text{floor is = mv= 10 kg × 4 ms}}^{\text{-1}}{\text{= 40 kgms}}^{\text{-1}}\text{.}\end{array}

As per the conservation of momentum,

(momentum of motorcar + momentum of insect)_before

 = (momentum of motorcar + momentum of insect)_after

∴ Change in in momentum = 0

The direction of the insect gets reversed when it stuck on the windscreen and the velocity of the insect changes to a great extend. The motorcar continues moving with a constant velocity in the forward direction.

As, Kiran suggested that the insect suffers a greater change in momentum as compared to the motorcar hence, it is correct. The momentum of the insect after collision becomes very high as the motorcar is moving at a very high speed. Therefore, the momentum gained by the insect is equal to the momentum lost by the motorcar.

Secondly, Akhtar is also correct as the mass of the motorcar is very large as compared to the mass of the insect and the speed of the motorcar is also very high.

Now, Rahul’s explanation is correct as both the car and the insect experienced equal forces caused by the Newton’s action-reaction law. But Rahul’s statement becomes incorrect when he said that the system suffers a change in momentum because the momentum before the collision is equal to the momentum after the collision.

$\begin{array}{l}\mathrm{Given},{\text{ inital velocity, u = 5 ms}}^{\text{-1}}\\ {\text{ final velocity, v = 8 ms}}^{\text{-1}}\\ \text{ mass , m = 100 kg}\\ \text{time taken by the object to accelerate, t = 6 s}\\ \\ \therefore \text{ Intial momentum = mu = 100}\times {\text{5 = 500 kgms}}^{\text{-1}}\\ \text{ Final momentum = mv = 100 }\times 8{\text{ = 800 kgms}}^{\text{-1}}\\ \mathrm{Force}\text{ exerted on the object, F =}\frac{\mathrm{mv}-\mathrm{mu}}{\mathrm{t}}\\ \text{ = }\frac{800-500}{6}\text{=}\frac{300}{6}\text{= 50 N. }\end{array}$

$\begin{array}{l}\mathrm{Given},\text{ mass of the object, m = 1 kg}\\ \text{mass of the wooden block, M = 5 kg}\\ \mathrm{velocity}{\text{ of the object before collision, u}}_{\text{1}}{\text{ = 10 ms}}^{\text{-1}}\\ \mathrm{velocity}{\text{ of the wooden block befor collision, u}}_{\text{2}}\text{ = 0}\\ \\ \mathrm{Total}\text{ momentum before collision,}\\ {\text{ P}}_{\text{inital }}={\text{ mu}}_{\text{1}}{\text{+Mu}}_{\text{2}}\text{ = 1}\times \text{10}+\text{5}\times 0=10{\text{ kgms}}^{\text{-1}}\\ \mathrm{After}\text{ collision, both the blocks stick together, hence}\\ \mathrm{the}\text{ the combined mass = M+m = 5+1 = 6 kg}\\ \text{Let, the velocity of the combined mass is V}\\ \text{Then, as per conservation law of momentum,}\\ {\text{ P}}_{\text{inital}}{\text{ = P}}_{\text{final}}\\ \text{ 10 = 6}\times \text{ V}\\ \text{or V = }\frac{10}{6}{\text{= 1.67 ms}}^{\text{-1}}\\ \text{Hence, the velocity of the combined mass after}\\ {\text{collision would be 1.67 ms}}^{\text{-1}}\text{. }\\ {\text{Now, final momentum, P}}_{\text{final}}\text{ = (M+m)V =6}\times \text{1.67}\\ {\text{ =10 kgms}}^{\text{-1}}\text{.}\end{array}$

The static friction acting between the truck and the road is very large as the truck is very massive. Thus, truck does not move when someone pushes it. Therefore, it can be concluded that the applied force in one direction is cancelled out by the frictional force of equal amount acting in the opposite direction.

When the force of 200 N is applied on wooden cabinet, an equal and opposite force acts on it. This opposite force is the frictional force. Therefore, a frictional force of 200 N is exerted on the cabinet.

\begin{array}{l}(a)\text{\hspace{0.17em}Given, }\text{force exerted by the engine, F = 40000 N}\\ \text{ frictional force due to tracks, F' = 5000 N}\\ \therefore {\text{ Net force, F}}_{\text{net}}=40000-5000\text{ = 35000 N}\\ \text{(b)}\text{Net force on the wagons},F_a=\text{ 35}000\text{ N}\\ \text{Mass of the 5 wagons},m=\text{2}000\times \text{5 }=\text{1}0000\text{ kg}\\ \text{Mass of the engine},m\prime =\text{ 8}000\text{ kg}\\ \therefore \text{ Total mass},\text{ M }=m+m\prime =\text{ 18}000\text{ kg} \\ \text{Using Newton}’\text{s second law of motion,}\\ {\text{ F}}_a=Ma\\ \text{or, a }\text{= }\frac{{\text{F}}_a}{M}\text{ = }\frac{35000}{18000}=\text{ 1}{\text{.944 ms}}^{\text{-2}}\\ \text{Hence, the acceleration of the wagons and the train is}\\ 1.944{\text{ ms}}^{\text{-2}}.\\ \end{array}

The correct option is (c)

Explanation: Here, the ball comes to rest due to frictional force which opposes its motion. Frictional force always acts in the direction opposite to the direction of motion. Therefore, this force tries to stop the ball.

Yes. It is possible that an object is moving with a non-zero velocity even when the object experiences a net zero external unbalanced force. It is possible only when the object has been moving with a constant velocity in a certain direction. In order to change the state of motion, a net non-zero external unbalanced force must be applied on the object.

When the bus starts accelerating in forward direction, it comes in the state of motion but the luggage kept on the roof remains in the state of rest. Therefore, with the forward movement of the bus, the luggage remains at its original position and finally falls from the roof of the bus. Hence, it is advised to tie any luggage kept on the roof of a bus.

Due to inertia, an object opposes any change in its state of rest or state of motion. As soon as the carpet is beaten with a stick, the carpet comes into motion while the dust particles oppose their state of rest. As per Newton’s first law of motion, the dust particles remain stationary, while the carpet moves. Therefore, the dust particles come out of the carpet.