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Given a=4.00 m/s2 m=1000kg Therefore , $F= ma= 1000 \times 4 =4000$ NQuestion 2 (a) 2 m/s2 (b) 30 m/s2 (c) 10 m/s2 (d) None of these. Solution Given F=3 Nm=.1 kg $F=ma$ or$a = \frac {F}{m}= 30$ m/s2 Question 3 A body of mass 1 kg undergoes a change of velocity of 4m/s in 4s what is the force acting on it?Solution Given $\Delta v=4 m/s$ ,t=4 s ,m=1kg Acceleration is given by $a= \frac {\Delta v}{t}$a=1 m/s2 Now force is given by$F=ma$ F=1 NQuestion 4. A particle of 10 kg is moving in a constant acceleration 2m/s2 starting from rest. What is its momentum and velocity per the table given below
Solution Velocity can find using $v=u+at$ For u=0 $v=at$ Momentum $P=mv$
Question 5 If a net force of 7 N was constantly applied on 400 g object at rest, how long will it take to raise its velocity to 80 m/s? a. 0 s b. 2.23 s c. 3.47 s d. 4.57 s Solution a=17.5 m/s2 Now u=0,v=80 m/s $v=u + at$ $t=\frac {v-u}{a}$t=4.57 sec Question 6 A sedan car of mass 200kg is moving with a certain velocity . It is brought to rest by the application of brakes, within a distance of 20m when the average resistance being offered to it is 500N.What was the velocity of the motor car? Solution $F=ma$ or $a= \frac {F}{m}$ ora= -500/200=-2.5 m/s2 Now $v^2=u^2 +2as$Now v=0,s=20 m,a=-2.5 m/s2 So, u=10 m/sQuestion 7 A driver accelerates his car first at the rate of 4 m/s2 and then at the rate of 8 m/s2 .Calculate the ration of the forces exerted by the engines? Solution $F_1= ma_1$ and $F_2=ma_2$ So,Ratio of force exerted is given by $=\frac {F_1}{F_2}=\frac {ma_1}{ma_2}=\frac {a_1}{a_2}= 1:2$ Question 8 An object of mass 10 g is sliding with a constant velocity of 2 m/ s on a frictionless horizontal table. The force required to keep the object moving with the same velocity is (a) 0 N (b) 5 N (c) 10 N (d)20 NSolution As m=0, F=0 Hence (a) is correctQuestion 9 A cricket ball of mass 0.20 kg is moving with a velocity of 1.2m/s . Find the impulse on the ball and average force applied by the player if he is able to stop the ball in 0.10s?Impulse= Change in momentum $I=\Delta p= m \Delta v= .20 \times 1.2=.12$ Kgm/s Now Impulse is also defined as $I=F \times t$ or $F \times t=.12$ or $F=\frac {.12}{.10}=1.2$ N Solution Question 10 Solution Given u=0 ,v= 54 km/hr= 15 m/s , t=2 sec a. Acceleration is given by $a=\frac {\Delta v}{t}$So, a=7.5 m/s2 b. Distance is given by $s=ut+ \frac {1}{2}at^2$ s= 15 m c. Force is given by $F=ma=1000 \times 7.5=7500$ NQuestion 11 A hockey ball of mass .2 Kg travelling at 10 ms-1 is struck by a hockey stick so as to return it along its original path with a velocity at 2 m/s . Calculate the change of momentum occurred in the motion of the hockey ball by the force applied by the hockey stick. Solution $ \Delta P= m \times (v - u) = 0.2 \times (-2 - 10) = -2.4$ kg ms-1 (The negative sign indicates a change in direction of hockey ball after it is struck by hockey stick. ) Question 12 Two objects of masses of 100 gm and 200 gm are moving in along the same line and direction with velocities of 2 ms-1 and 1 ms-1 respectively. They collide and after collision, the first object moves at a velocity of 1.67 ms-1. Determine the velocity of the second object? Solution Given $m_1 = 100 gm = 0.1 kg$, $m_2 = 200 gm = 0.2 kg$ $u_1 = 2$ ms-1, $u_2 = 1$ ms-1, $v_1 = 1.67$ ms-1, $v_2 = ?$ By the law of conservation of momentum, $m_1 u_1+m_2 u_2=m_1 v_2 + m_2 v_2$ $0.1 \times 2+ 0.2 \times 1=0.1 \times 1.67 + 0.2 v_2$$v_2 = 1.165$ ms-1 It will move in the same direction after collisionQuestion 13 Anand leaves his house at 8.30 a.m. for his school. The school is 2 km away and classes start at 9.00 a.m. If he walks at a speed of 3 km/h for the first kilometre, at what speed should he walk the second kilometre to reach just in time?Question 14 An object of mass 1kg acquires a speed of 10 m/s when pushed forward. What is the impulse given to the object?Solution Impulse=Change in Momentum= 10 Kgm/sQuestion 15 Solution Let v be the initial recoil velocity of the rifle From law of conservation of Momentum $0=.01 \times 20 + 4 \times v$ Or $v=-.05 m/s$Question 16 Velocity versus time graph of a ball of mass 100 g rolling on a concrete floor is shown below. Calculate the acceleration and the frictional force of the floor on the ball?
Solution From the graph ,we can see that $\Delta v=-80 m/s$, t=8 sec Now $a= \frac {\Delta v}{t} = -10 m/s^2$ Frictional force will be given as $F= ma= .1 \times -10 = -1 N$ Question 17 Which would require a greater force �� accelerating a 2 kg mass at 5 m/s2 or a 6 kg mass at 2 m/s2? Solution we have $F = ma$. Here we have $m_1 = 2$ kg and $a_1 = 5 m/s^2$ and $m_2 = 6$ kg and $a_2 = 2 m/s^2$ . So, $F_1 = m_1a_1 = 2 \times 5 = 10 N$ $F_2 = m_2a_2 = 6 \times 2 = 8 N$. Here $F_1 < F_2$ Thus, accelerating a 6 kg mass at 2 m/s2 would require a greater force Question 17 An object of mass 2 kg is sliding with a constant velocity of 8 m/s on a frictionless horizontal table. The force required to keep the object moving with the same velocity is (a) 16 N (b) 8 N (c) 2 N (d) 0 NSolution (d) as there is no friction forceDownload force and laws of motion class 9 numericals pdf link to this page by copying the following text <a href="https://physicscatalyst.com/Class9/force_numericals.php">Sure shot Numericals on Force And Laws of Motion| Class 9 physics notes| Class 9 Science notes</a> Also Read Class 9 Maths Class 9 Science |