A force \(\vec{A}=\left(10\hat{i}-6\hat{j}+8\hat{k}\right)N\) produces an acceleration of \(1 ms^{-2}\) in a body of mass \(m\). Calculate: Magnitude of m?
Ans: \(a=1\frac{m}{s^{2}}\) and \(m=14.14Kg\).
A force acts for \(10Sec\) on a body of mass \(10kg\) after which the force ceases to act and the body covers \(50m\)in next \(5Sec\). Find: the magnitude of the force.
Ans: \(F=10N\).
A force of \(5N\) gives a mass \(m_{1}\), an acceleration of \(8ms^{-2}\) and a mass \(m_{2}\) an acceleration of \(24ms^{-2}\). What acceleration it will give if the both masses are joined together?
Ans: \(a=6\frac{m}{s^{2}}\).
The motion of a particle of mass \(m\) is described by \(y=ut+\frac{1}{2}at^{2}\). Find: the force acting on it?
Ans: \(F=mg\).
The force on a particle of mass \(10g\) is \(\left(10\hat{i}+5\hat{j}\right)N\). If, it starts from rest, what would be the position at time \(t=5Sec\).
A stone of mass \(5kg\) falls from top of a cliff \(50m\) high and buries under the sand to \(1m\). Find: the average resistance offered by the sand to the motion of stone and the time stone takes to penetrate \(1m\) in to the sand?
Ans: \(a=-490\frac{m}{s^{2}}\) and \(t=0.064s\).
A motor car is running at a rate of \(7ms^{-1}\) can be stopped by applying breaks in \(10m\). Show that total resistance offered by the breakes to the motion of motor car is \(\left(\frac{1}{4}\right)^{th}\) times the weight of the car.
A balloon has a mass of \(5g\) of air filled inside it. The air escapes from the balloon at a uniform rate with a velocity of \(5cm.s^{-1}\). If the balloon shrinks completely in \(2.5Sec\), what will be average force acting on the balloon?
Ans: \(F=10dyne\).
A body of mass \(m\) moves along X-axis such that its position coordinates at any instant \(t\) is \(x=at^{4}-bt^{3}+ct\) where a, b, c are constants. What is the force acting on the particle at any instant?
Ans: \(F=m\left(12at^{2}-6bt\right)Units\).
A force of \(50N\) is inclined to the vertical at an angle of \(30^{o}\). Find: the acceleration it produces in the body of mass \(2kg\) which moves in horizontal direction.
Ans: \(a=12.5\frac{m}{s^{2}}\).
A bullet of mass \(200g\) fired from a gun moving with a velocity \(20 ms^{-1}\) hits a wooden log. The bullet stops after travelling a distance of \(40cm\) in the wooden log. Calculate: the retarding force exerted by the log on the bullet?
Ans: \(F=-100N\)
Two mutually perpendicular forces \(8N\) and \(6N\) acts on the same body of mass \(10kg\).Calculate: (i) Net Force acting on the body? (ii) Magnitude of the acceleration of the body? and (iii) Direction of acceleration of the body?
Ans:(i) \(F=10N\), (ii) \(a=1\frac{m}{s^{2}}\) and \(36^{o}\).
A \(600kg\) rocket is set for a vertical launching. If, the exhaust speed is \(1000 ms^{-1}\), then what is the amount of gases ejected per second to supply the thrust needed to overcome the weight of the rocket? (Take: \(g=10ms^{-2}\))
A scotterist is moving with a velocity \(36km.h^{-1}\) sees a child standing in the middle of the road. He applies the breaks and bring the scooter to rest in \(5Sec\) just in time to save the child. Calculate: the average retarding force on the vehicle, if mass of the vehicle and driver is \(300kg\).
