The figure shows a horizontal force $\vec F$ acting on the block of mass $M$ on an inclined plane (angle $\theta $ ). What is the normal reaction $N$ on the block?
A) $mg\,\sin \theta + F\,\cos \theta $
B) $mg\,\sin \theta - F\,\cos \theta $
C) $mg\,\cos \theta - F\sin \theta $
D) $mg\,\cos \theta + F\,\sin \theta $
Answer
Verified
120.6k+ views
Hint: Construct the diagram of the horizontal force given and also the force due to the weight of the block taken. Split these two forces into horizontal components and the vertical component to obtain the resultant force and the normal force to it.
Complete step by step solution:
It is given that the
Horizontal force acting on the block is $\vec F$
The mass of the block is $M$
The mass is at an angle of $\theta $ on the inclined plane
Since $\vec F$ is the horizontal force that acts on the block, it pushes the block to move upward on the slanting inclined plane. There will be the force which acts against it and downwards. It is formed by the combination of the weight of the block and the gravitational force of the block towards the earth. According to Newton's second law of motion, force is the product of the mass and the acceleration.
${F_w} = mg$
This force pulls the block towards down against the horizontal external force. Let us construct the diagram of the case given.
From the constructed diagram, the force $mg$divided into $mg\,\sin \theta $ and $mg\,\cos \theta $. And the horizontal force divided into $F\sin \theta $ and $F\,\cos \theta $ . If we take the normal, the answer is $mg\,\cos \theta + F\,\sin \theta $.
Thus the option (D) is correct.
Note: It is to be noted that when the vector of the force is divided into the horizontal and the vertical component, the sine of the force magnitude is taken as the vertical component of force and the cosine is taken as the horizontal component.
Complete step by step solution:
It is given that the
Horizontal force acting on the block is $\vec F$
The mass of the block is $M$
The mass is at an angle of $\theta $ on the inclined plane
Since $\vec F$ is the horizontal force that acts on the block, it pushes the block to move upward on the slanting inclined plane. There will be the force which acts against it and downwards. It is formed by the combination of the weight of the block and the gravitational force of the block towards the earth. According to Newton's second law of motion, force is the product of the mass and the acceleration.
${F_w} = mg$
This force pulls the block towards down against the horizontal external force. Let us construct the diagram of the case given.
From the constructed diagram, the force $mg$divided into $mg\,\sin \theta $ and $mg\,\cos \theta $. And the horizontal force divided into $F\sin \theta $ and $F\,\cos \theta $ . If we take the normal, the answer is $mg\,\cos \theta + F\,\sin \theta $.
Thus the option (D) is correct.
Note: It is to be noted that when the vector of the force is divided into the horizontal and the vertical component, the sine of the force magnitude is taken as the vertical component of force and the cosine is taken as the horizontal component.
Recently Updated Pages
Structure of Atom: Key Models, Subatomic Particles, and Quantum Numbers
Difference Between Circuit Switching and Packet Switching
Difference Between Mass and Weight
JEE Main Participating Colleges 2024 - A Complete List of Top Colleges
Sign up for JEE Main 2025 Live Classes - Vedantu
JEE Main 2025 Exam Pattern: Marking Scheme, Syllabus
Trending doubts
Learn About Angle Of Deviation In Prism: JEE Main Physics 2025
Charging and Discharging of Capacitor
JEE Mains 2025 Correction Window Date (Out) – Check Procedure and Fees Here!
JEE Main 2022 June 25 Shift 2 Question Paper with Answer Keys & Solutions
JEE Main Maths Paper Pattern 2025
Electromagnetic Waves Chapter - Physics JEE Main
Other Pages
NCERT Solutions for Class 11 Physics Chapter 9 Mechanical Properties of Fluids
Thermodynamics Class 11 Notes CBSE Physics Chapter 11 (Free PDF Download)
Mechanical Properties of Fluids Class 11 Notes CBSE Physics Chapter 9 (Free PDF Download)
JEE Advanced 2025 Revision Notes for Physics on Modern Physics
JEE Main 2025 Helpline Numbers for Aspiring Candidates
JEE Advanced 2025 Revision Notes for Practical Organic Chemistry