Numerical Problems (Solved): Force and Newton's Law of Motion | Science Class 9 PDF Download

Q1: A cricket ball of mass 70 g moving with a velocity of 0.5 m s^-1 is stopped by player in 0.5 s. What is the force applied by player to stop the ball?  
Sol. Here m = 70 g = 0.070 kg; u = 0.5 m s^-1; v = 0; t = 0.5 s 

Q2: What will be acceleration of a body of mass 5 kg if a force of 200 N is applied to it?  
Sol. Here m = 5 kg; F = 200 N 
 F = ma or a = F/m 
 

Q3: A bullet of mass 10 g is fired from a rifle. The bullet takes 0.003 s to move through its barrel and leaves with a velocity of 300 ms^-1. What is the force exerted on the bullet by the rifle?  
Sol. Here m = 10 g = 0.010 kg ; u = a ; v = 300 m s^-1 
 t = 0.003 s, F = ? 

Q4: What force would be needed to produce an acceleration of 1 ms^-2 on a ball of mass 1 kg?  
Sol. Here m = 1 kg; a = 1 ms^-2 ; F = ? 
 Now F = m a = 1 × 1 
 or F = 1 newton. 

Q5: What is the acceleration produced by a force of 5 N exerted on an object of mass 10 kg?  
Sol. Here F = 5 N; m = 10 kg; a = ? 
 Now F = ma o
 a = 0.5 ms^-2  

Q6: How long should a force of 100 N act on a body of 20 kg so that it acquires a velocity of 100 ms^-1?  
Sol. Here v _ u = 100 m s^-1, m = 20 kg; F = 100 N ;t = ? 
We know 

Q7: Which would require greater force: accelerating a 10 g mass at 5 m s^_2 or 20 g mass at 2 m s^-2?  
Sol. In first case m₁ = 10 g = kg = 0.010 kg; 
 Now a₁ = 5 ms^-2 ; F₁ = ? 
 F₁ = m₁a₁ = 0.010 × 5
 F₁ = 0.050 newton 
 In second case, m₂ = 20 g =0.020 kg 
 or m₂ = 0.020 kg 
 a₂ = 2 m s^-2 ; F₂ = ? 
 Now F₂ = m₂a₂ = 0.020 × 2 
 or F₂ = 0.04 newton 
 We find that F₁ > F₂, hence more force is required to accelerate 10 g at 5 m s^-2 than accelerating 20 g at 2 ms^-2.  

Q8: A force of 5 N gives a mass m₁, an acceleration of 8 ms^-2 and a mass m₂, an acceleration of 24 m s^-2. What acceleration would it give if both the masses are tied together?  
Sol. Let us first find mass m₁ and m₂. 
F = m₁ a₁ 
5 =m₁ (8) or m₁ = 5/8 kg 
F = m₂ a₂ 
5 = m₂ (24) or m₂ = 5/24 kg 
Total mass M = m₁ + m₂ 

Let A be the acceleration produced in mass M. 
F = MA 

Hence the acceleration of the combination is 6 ms^-2. 

Q9: If 1000 N force is required to accelerate an object to the rate of 5m/s2, what will be the weight of the object?

Sol: According to question 

Q10: After applying a force of 1000 N an object of mass 2000 kg will achieve what acceleration?

Sol: