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NCERT Exemplar · Class 9 Science Force and Laws of Motion

20 questions · 20 still being checked

Short Answer Questions 9–17 (part 2 of 3)

  1. Exercise 9

    There are three solids made up of aluminium, steel and wood, of the same shape and same volume. Which of them would have highest inertia?

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    NCERT’s answer
    Steel. As the mass is a measure of inertia, the ball of same shape and size, having more mass than other balls will have highest inertia. Since steel has greatest density and greatest mass, therefore, it has highest inertia.
    Inertia is simply mass; equal volumes make mass track density alone. \[m = \rho V, \quad V \text{ same for all three} \] \[\rho_{\text{steel}} > \rho_{\text{aluminium}} > \rho_{\text{wood}} \] The densest of the three therefore carries the largest mass. Answer: Steel has the highest inertia — same volume, but steel's greater density gives it the greatest mass.

  2. Exercise 10

    Two balls of the same size but of different materials, rubber and iron are kept on the smooth floor of a moving train. The brakes are applied suddenly to stop the train. Will the balls start rolling? If so, in which direction? Will they move with the same speed? Give reasons for your answer.

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    \[\text{brakes} \Rightarrow v_{\text{train}}\downarrow; \qquad F_{\text{ball}}=0 \Rightarrow a_{\text{ball}}=0\ \text{for any mass } m \] The smooth floor exerts no horizontal force on either ball, so each keeps the train's earlier speed whatever its mass — mass cancels out of \(\displaystyle a=F/m=0\). Relative to the slowing train, both slide forward toward the engine, since there is no friction to make them roll.Answer: Yes, they move (sliding, since the floor is smooth), forward toward the engine, at the same speed whatever the material.NCERT prints: "the balls will start rolling ... since the masses of the balls are not the same ... the balls will move with different speeds" — a misprint twice over: a smooth floor exerts no friction or torque, so the balls slide rather than roll, and \(\displaystyle a=F/m=0\) for both regardless of mass, so they move at the same speed.

  3. Exercise 11

    Two identical bullets are fired one by a light rifle and another by a heavy rifle with the same force. Which rifle will hurt the shoulder more and why?

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    NCERT’s answer
    From the light rifle, according to law of conservation of momentum or explanation by Newton’s laws of motion.
    The same force is the reaction each rifle feels on firing (Newton's third law). \[F = Ma \Rightarrow a = \frac{F}{M} \] \[M_{\text{light}} < M_{\text{heavy}} \Rightarrow a_{\text{light}} > a_{\text{heavy}} \] Over the same short firing time this gives the light rifle a larger recoil velocity. Answer: The light rifle hurts the shoulder more; the same force on its smaller mass produces a greater recoil acceleration and speed.

  4. Exercise 12

    A horse continues to apply a force in order to move a cart with a constant speed. Explain why?

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    NCERT’s answer
    The force applied by the horse balances the force of friction.
    Constant speed means zero acceleration, so the net force on the cart must be zero. \[v = \text{const} \Rightarrow a = 0 \Rightarrow F_{net} = 0 \] \[F_{\text{horse}} - f_{\text{friction}} = 0 \Rightarrow F_{\text{horse}} = f_{\text{friction}} \] Friction at the wheels and axle keeps opposing the motion, so the pull can never be withdrawn. Answer: The horse's force only balances friction; removing it would make the net force nonzero and slow the cart down.

  5. Exercise 13

    Suppose a ball of mass m is thrown vertically upward with an initial speed v, its speed decreases continuously till it becomes zero. Thereafter, the ball begins to fall downward and attains the speed v again before striking the ground. It implies that the magnitude of initial and final momentums of the ball are same. Yet, it is not an example of conservation of momentum. Explain why ? FORCE AND LAWS OF MOTION

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    NCERT’s answer
    Law of conservation of momentum is applicable to isolated system (no external force is applied). In this case, the change in velocity is due to the gravitational force of earth.
    Momentum is a vector: matching magnitudes does not mean matching momenta. \[p_i = +mv \quad (\text{upward, at launch}) \] \[p_f = -mv \quad (\text{downward, at landing}) \] \[p_i \neq p_f, \ \text{though} \ |p_i| = |p_f| \] \[\frac{dp}{dt} = F_{net} = -mg \neq 0 \quad \text{throughout the flight} \] Answer: No — momentum is a vector; gravity (a nonzero net force) reverses it from \(\displaystyle +mv\) to \(\displaystyle -mv\), so equal magnitude is not conserved momentum.

  6. Exercise 14

    Velocity versus time graph of a ball of mass 50\displaystyle 50 g rolling on a concrete floor is shown in Fig. 9.1. Calculate the acceleration and frictional force of the floor on the ball. NCERT_Question_Class9_Science_Exemplar_Ch9_Q14

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    NCERT’s answer
    Acceleration = a = - v u t $\displaystyle 80$ ms —10ms − − = − = Force = m a = $\displaystyle 50$ 0.5N $\displaystyle 1000$ × =
    The graph is a straight line from \(\displaystyle 80\ \text{m s}^{-1}\) at \(\displaystyle t=0\) to \(\displaystyle 0\) at \(\displaystyle t=8\ \text{s}\); its slope is the (constant) acceleration. \[a=\dfrac{v-u}{t}=\dfrac{0-80\ \text{m s}^{-1}}{8\ \text{s}-0}=-10\ \text{m s}^{-2} \] Friction is the only horizontal force on the rolling ball, so by Newton's second law: \[m=50\ \text{g}=0.050\ \text{kg} \] \[F=ma=0.050\ \text{kg}\times10\ \text{m s}^{-2}=0.5\ \text{N} \] The minus sign in \(\displaystyle a\) shows the force acts opposite to the ball's motion, slowing it down.Answer: \(\displaystyle a=-10\ \text{m s}^{-2}\); frictional force \(\displaystyle =0.5\ \text{N}\), directed opposite to the motion.

  7. Exercise 15

    A truck of mass M is moved under a force F. If the truck is then loaded with an object equal to the mass of the truck and the driving force is halved, then how does the acceleration change?

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    NCERT’s answer
    Calculate using F= m a Acceleration becomes one-fourth of the original.
    Acceleration is force over mass; both the mass and the force change together. \[a = \frac{F}{M} \] \[a' = \frac{F/2}{M+M} = \frac{F}{4M} = \frac{a}{4} \] Loading doubles the mass while the push is only halved, so the two changes compound. Answer: The acceleration falls to one-quarter of its original value.

  8. Exercise 16

    Two friends on roller-skates are standing 5\displaystyle 5 m apart facing each other. One of them throws a ball of 2\displaystyle 2 kg towards the other, who catches it, How will this activity affect the position of the two? Explain your answer.

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    NCERT’s answer
    Separation between them will increase. Initially the momentum of both of them are zero as they are at rest. In order to conserve the momentum the one who throws the ball would move backward. The second will experience a net force after catching the ball and therefore will move backwards that is in the direction of the force.
    Momentum is conserved in each exchange: zero for thrower + ball, \(\displaystyle m\,v_{ball}\) for ball + catcher. \[0 = m\,v_{ball} + M_A v_A \Rightarrow v_A = -\frac{m}{M_A}v_{ball} \] \[m\,v_{ball} + M_B(0) = (M_B+m)v_B' \Rightarrow v_B' = \frac{m\,v_{ball}}{M_B+m} \] A recoils away from B on throwing; B is pushed further away from A on catching.Answer: Both skaters recoil apart from each other — the thrower backward on release, the catcher backward on impact — so their separation grows beyond the original $\displaystyle 5$ m.

  9. Exercise 17

    Water sprinkler used for grass lawns begins to rotate as soon as the water is supplied. Explain the principle on which it works.

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    NCERT’s answer
    The working of the rotation of sprinkler is based on third law of motion. As the water comes out of the nozzle of the sprinkler, an equal and opposite reaction force comes into play. So the sprinkler starts rotating.
    Water squirts out of each bent nozzle tip in one tangential direction. \[F_{\text{jet on arm}} = -F_{\text{arm on jet}} \quad (\text{Newton's third law}) \] This reaction force acts tangentially at each arm, about the central pivot, so it turns the whole sprinkler.Answer: The reaction (Newton's third law) to water jetting out tangentially from the bent arms pushes the arms — and so the sprinkler — around in the opposite sense.