GATE ME 2026 Set 1 — Question 48
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.NAT+2 / -0MediumFree-Body Diagrams & EquilibriumStaticsEngineering MechanicsFriction & Applications
Engineering Mechanics → Statics → Free-Body Diagrams & Equilibrium
Last updated
Question
A block of kg mass is on an inclined plane. The block is connected to another hanging mass by an inextensible massless string through two massless pulleys as shown in the figure below. The coefficient of static friction between the block and the inclined plane is . Neglecting pulley friction, the minimum value of required to start the upward motion of the block is ________ kg (rounded off to decimal place).
Correct answer
18.5 to 19.5
Solution
To find the minimum mass required to start the upward motion of the kg block, we analyze the forces at the point of impending motion.
Let be the tension in the string. For the hanging mass in equilibrium:
The movable pulley attached to the block is pulled by two segments of the same string. Thus, the total upward force along the incline is:
At the verge of moving up the incline, the upward force must balance the downward forces (weight component and maximum static friction):
Dividing by :
1.Analyze the Pulley System:
The string is fixed at the top, goes around a movable pulley attached to the kg block, and then over a fixed pulley to the hanging mass . Let be the tension in the string. For the hanging mass in equilibrium:
The movable pulley attached to the block is pulled by two segments of the same string. Thus, the total upward force along the incline is:
2.Analyze the Forces on the 50 kg Block:
- Mass of the block kg
- Angle of inclination
- Coefficient of static friction
- Normal force
- Frictional force (opposing upward motion)
- Component of weight down the incline
At the verge of moving up the incline, the upward force must balance the downward forces (weight component and maximum static friction):
Dividing by :
4.Calculation:
Rounding to decimal place, the minimum value of is kg.Continue learning with Success Tracker
A step still unclear? Work through it with support
Use Success Tracker to ask about the reasoning, then try another GATE ME question to check your understanding.
AI-powered practice· Unlimited practice on eligible plans
- PYQs with solutions
- Attempt available previous-year questions, then compare your reasoning with the worked solution. Coverage varies by stream.
- Practice that adapts
- Choose a topic, work on weaker areas and bookmark questions to revisit. Your attempts feed your progress tracking.
- AI doubt support
- Ask follow-up questions about a step or concept while practising, instead of stopping at the final answer.
Unlimited practice is available on eligible plans. Free practice and AI usage have limits; check the current plan allowances before choosing.
This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.
More questions on Statics
2026 Set 1 Q16A horizontal disk has a radial frictionless slot in which a small block is confined to slide. The…2026 Set 1 Q29A hydraulic crane supports a mass of with its piston-cylinder actuator, inclined at…2026 Set 1 Q41Two structural members are connected by a hinge and they are externally loaded as shown in the…2026 Set 1 Q50A rigid slender bar, AB, is sliding against two mutually perpendicular frictionless walls, as shown…2025 Set 1 Q26A rigid circular disc of radius (in m) is rolling without slipping on a flat surface as shown…