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Correct OPTION is (a) Momentum

Easy explanation: Two bodies collide in the absence of any EXTERNAL force. In this CASE the momentum will remain constant because there is no force, hence, there is no CHANGE in momentum. The velocity and speed of the bodies might change after COLLISION.

Correct answer is (b) SUM of all MOMENTS on a body should be zero

To elaborate: The SECOND CONDITION for a body to exist in EQUILIBRIUM is that the sum of all moments on the body must be zero. Which means that the resultant moment on a body should be zero.

The correct answer is (b) \(\VEC{F1} = -\vec{F2}\)

Easiest explanation: According to the third law of MOTION, every action has an equal and opposite reaction. Hence every action force is equal in MAGNITUDE to its reaction but in opposite direction. Hence \(\vec{F1} = -\vec{F2}\) is the correct answer.

Right choice is (b) DECREASE with time

For EXPLANATION I would say: As the other end of the string is fixed to the wooden bar, the motion will cause the string to wrap itself around the bar. This will result in decrease in the effective radius of the CIRCULAR motion. Tangential VELOCITY V = ωr, the tangential velocity will decrease with time.

The correct option is (c) The mass of the body is negligible as compared to the mass of the wall or the GROUND

For explanation I would SAY: When a body collides with a wall or the ground, we CONSIDER that the mass of the body is negligible as compared to the mass of the wall or the ground. We also make this ASSUMPTION when something like a feather, which has a very SMALL mass collides with a truck, which, comparatively, has a huge mass.

Correct CHOICE is (a) 4/3

The EXPLANATION: The angular velocity is given as, ω = v/r. HENCE, the function for angular velocity is ω = (7t^2 – 2)/21. On differentiating this expression, we will get the angular acceleration as t^2/3 On substituting, the suitable values, we will get the angular acceleration as 4/3 rad/s^2.

The correct answer is (a) ENERGY

For explanation I would say: Apart from the momentum, the energy ALSO REMAINS conserved during collision. As a MATTER of fact, the energy of a system OFTEN remains conserved.

Right answer is (c) PROPERTY of mass to accelerate

Best explanation: Inertia is the property of mass to remain UNCHANGED. Inertia is because of which a mass continues to remain in its ORIGINAL state in absence of any external force. Inertia of a body can be CHANGED only by an external force.

Correct CHOICE is (a) -5/3

Best explanation: The angular VELOCITY is given as, ω = v/r. Hence, the FUNCTION for angular velocity is ω = (2t^2 – 7)/3. On substituting, the SUITABLE values, we will get the angular velocity as -5/3 rad/s.

Correct option is (b) 5 Kg

The best explanation: The body is MOVING in the absence of any EXTERNAL force thus the momentum remains conserved. M1V1 = m2v2. v1 = 7 m/s, m1 = 10 Kg, v2 = 14 m/s. On solving, we GET, m2 = 5 kg. Hence, the correct ANSWER is 5 Kg.

Correct choice is (b) A rocket taking off

To ELABORATE: In case of a rocket taking off, the mass of the fuel is LARGE and cannot be neglected. As the rocket starts MOVING, a large amount of fuel is getting burnt out from the nozzle, hence the TOTAL mass decreases. Hence it is a variable mass system.

Right answer is (a) Inertia of motion

To explain: When the bus stops, the people SITTING in it experience a JERK. This is because, while the bus was moving, the people were moving with it. HENCE, they were having an inertia of motion. When the bus stops, the inertia of the bus changes from that of motion to that of rest. But the inertia of the people STILL remains that of motion. Hence, they experience a jerk.

The correct CHOICE is (a) At 10 s

Explanation: The centripetal force on a body is directly proportional to its mass with a PROPORTIONALITY constant of 1. Hence the centripetal force will be zero when the mass is zero. The function for the mass at t seconds is m = 5 – 0.5t. On EQUATING this to zero we GET, t = 10 s. this is the required time.

Correct answer is (a) Stable EQUILIBRIUM

Easy EXPLANATION: The BODY is said to be in the state of stable equilibrium if it returns to its original equilibrium after giving it a SLIGHT displacement. In UNSTABLE equilibrium, the body does not return to its original equilibrium and moreover also does not achieve any other equilibrium. In neutral equilibrium, the body attains a new equilibrium every time it is displaced.

Right option is (a) 7î – 13Ĵ

The best I can EXPLAIN: For the BODY to remain in equilibrium, the total force on it should be zero. As one of the forces is given, the other force can be found out by subtracting it from zero. Hence the answer is -7î + 13ĵ.

The correct choice is (a) 2.5 Kg

For EXPLANATION I would say: From the second law of motion we get that F = ma, when the mass is not changing. Putting in the values, we get, Force = 10 = m X 4. Which will RESULT in m = 2.5 Kg.

The correct choice is (a) Equal in magnitude and opposite in direction

For EXPLANATION: Only when the forces are equal in magnitude and opposite in direction, the net FORCE will be ZERO on the BODY. Since there is no moment, we need not care about the SECOND condition of equilibrium. The body is in equilibrium only when the net force acting on it is zero which is satisfied only in this manner.

Right CHOICE is (a) 35 N

Explanation: ACCORDING to the second law of MOTION, the force on a BODY is equal to the rate change of its momentum. On simplifying we get, F = ma. Therefore, Force = 5 x 7 = 35 N.

Right answer is (c) F = v(dm/dt) + ma

To EXPLAIN I would say: The second law of motion states that the net force applied on a body is EQUAL to the rate of change of momentum. Hence, F = dp/dt. p = mv. THEREFORE, F = m(dv/dt) + v(dm/dt) = v(dm/dt) + ma.

Right answer is (a) Force

Best EXPLANATION: The first LAW of motion states that a body remains in the STATE of motion or in the state of rest until and UNLESS an EXTERNAL force is applied on it. Hence, the answer is force. This is also known as the law of inertia.

The CORRECT answer is (a) It increases

The explanation: When the ROCKET is in the ORBIT with the THRUSTERS on, there is a tangential force that the rocket experiences. This force will result in increasing the tangential velocity. Since the angular velocity is directly proportional to the tangential velocity, the angular velocity will ALSO increase.

Right ANSWER is (a) The total momentum remains CONSERVED about the instant of collision

For EXPLANATION I would say: The TWO bodies are accelerating and they collide. Since they are accelerating the total momentum does not remain conserved during the motion. But at the instant of collision, both the bodies have a CONSTANT velocity. Hence, just before and just after the collision, the total momentum will remain conserved.

The CORRECT answer is (a) 100 N

The explanation: From Newton’s THIRD law we know that for every for every action, there is an equal and opposite reaction. From this we can say that the car experiences a force of 100 N by the light pole.

The correct OPTION is (b) They are different in magnitude

The explanation: From the third law of motion, we KNOW that the cause force and the reaction forces are equal in magnitude and opposite in DIRECTION. Hence, from this KNOWLEDGE, we can say that the MAN and the kid will experience forces in opposite directions and in equal magnitude.

Right answer is (a) F = dp/dt

Explanation: The second law of motion states that the net force applied on a BODY is equal to the RATE of CHANGE of momentum. Momentum is usually represented by ‘p’. HENCE, the answer is F = dp/dt.

The correct answer is (b) Skiing

The best explanation: The THIRD law of motion does not apply to skiing as in skiing we do not apply any force on the ground. The motion is caused by GRAVITY and EXTREMELY less friction. In all the other cases, a force is APPLIED on the ground or the other body, the reaction of which CAUSES the motion.

Correct option is (a) MOMENTA

Easiest explanation: The plural for momentum is momenta and not momentums. Momenta, being a plural, is USUALLY USED in cases where we NEED to address a more than one momentum. This situation can possibly arise in systems having more than one moving BODY.

Correct option is (a) Spiral motion

To elaborate: A ball, tied to a ROPE, rotating around a fixed SUPPORT will CAUSE the rope to wind itself around the support. Hence, the motion will be circular with decreasing RADIUS. This motion will cause the path look like a spiral. Hence the motion is spiral in NATURE.

The correct choice is (a) 2.5 Kg

For explanation I would SAY: The body is moving in the absence of any EXTERNAL force THUS the momentum remains conserved.m1v1 = m2v2. v1 = 5 m/s, m1 = 5 Kg, V2 = 10 m/s. On solving, we get, m2 = 2.5 kg. Hence, the correct ANSWER is 2.5 Kg.

Correct choice is (B) Opposite directions

Easy explanation: The TWO bodies in contact will FOLLOW Newton’s third LAW of motion. The third law states that for every action there is an equal and opposite reaction. The two bodies will experience each other’s reaction forces in opposite directions.

Correct OPTION is (a) 10 m/s^2

The best explanation: From the second LAW of motion we get that F = ma, when the MASS is not changing. Putting in the values, we get, FORCE = 10 = 5 X a. Which will result in a = 10 m/s^2.

Correct option is (b) They will tilt leftwards

Easy explanation: When the bus takes a sharp right TURN, the inertia of the bus changes. But the inertia of the passengers is STILL TOWARDS the straight direction. Hence, they will relatively move towards the LEFT.

The correct choice is (b) MOVE backwards

Explanation: The third law of motion applies in this CASE. According to the third law of motion, for every ACTION, there is an equal and opposite reaction. When we WALK on the boat, the boat experiences an equal and opposite reaction force. Since very little resistance is offered by the still WATER, the boat will move backwards.

Correct option is (a) 112

To EXPLAIN: The tangential velocity is given as V = ωr. At t = 2s, r = 16 UNITS. The angular velocity is 7 rad/s. Hence, the tangential velocity, v = 7 x 16 = 112 units/s.

The CORRECT option is (a) -9î + 24ĵ

The best explanation: For the body to remain in equilibrium, the total force on it should be ZERO. As TWO of the forcesare given, the other force can be found out by SUBTRACTING the sum of both the given forces from zero. Hence the answer is -9î + 24ĵ.

Correct answer is (b) On different objects

The best I can explain: The TWO forces involved in NEWTON’s third law are the cause force and the REACTION force. The cause force acts on the contact SURFACE or the contact body by the parent body. Whereas the reaction force acts on the parent body by the contact body.

Correct choice is (a) SUM of all force on a body should be zero

Explanation: The first condition for a body to EXIST in equilibrium is that the sum of all FORCES on the body must be zero. Which means that the RESULTANT force on a body should be zero.

The correct choice is (a) Newton

To explain I WOULD say: The UNIT of force is newton. This unit has been GIVEN after the name of the famous scientist Sir Isaac Newton who had given the three laws of motion. The force on anybody can be found with the HELP of the second law of motion.

The correct CHOICE is (a) The VECTOR sum of the forces is zero

Explanation: When a body is in EQUILIBRIUM, the sum of all the forces is zero. The sum of all the forces RELATES to the vector sum of all the forces and not any other sum. The scalar sum is always positive hence it cannot be zero. The forces NEED not be zero for the body to be in equilibrium, only the vector sum has to be zero. The same goes with the magnitude and direction of the forces.

The correct option is (b) It is in dynamic equilibrium

The explanation is: When a BODY is moving with constant velocity, there is no net FORCE or MOMENT acting on it. Hence, the body is in equilibrium. But SINCE the body is moving, the equilibrium is KNOWN as dynamic equilibrium. Static equilibrium occurs when the body is at rest.

Right choice is (c) Third Law

The best EXPLANATION: The third law of motion states that for every action there is an equal and OPPOSITE reaction. This law helps us in finding the reaction forces on a body. A classic example is the WAY we walk. We need to push the ground for WALKING and when we do so we experience an equal and opposite FORCE on ourselves which helps us in walking.

Correct answer is (a) 12500 N

To explain: From Newton’ second law we get FORCE on scooter = 2500 x 5 = 12500 N. From Newton’s third law we know that for every for every ACTION, there is an equal and opposite reaction. From this we can SAY that the TRUCK experiences a force of 5 N.

Right answer is (b) Positive

To ELABORATE: The force has to be positive. The reason is that the forces are acting in opposite directions. Which means that the direction of the forces has been specified and they are bound to CANCEL each other out. So, if, the second force is negative, the net direction will be towards right and the BODY will not be able to stay in EQUILIBRIUM.

The correct option is (b) INERTIA of rest

Best EXPLANATION: When the car starts, the people sitting in it EXPERIENCE a jerk. This is because, while the car was stationary, the people were stationary with it. Hence, they were having an inertia of rest. When the car starts, the inertia of the car changes from that of rest to that of motion. But the inertia of the people still REMAINS that of rest. Hence, they experience a jerk.