HC Verma Chapter 5 Problem 33 — Hanging block with string: string breaks

Problem Statement

A 5 kg block hangs from a string (max tension 60 N). An additional 1 kg mass is placed on it suddenly. Will the string break? ($g = 10$ m/s²)

Given Information

• All quantities, constants, and constraints stated in the problem above
• Physical constants used as needed (see Concepts section)

Physical Concepts & Formulas

This problem draws on fundamental physical principles. The key is to identify which conservation law or field equation governs the system, then apply it systematically. Dimensional analysis can always be used to verify that the final answer has the correct units. Working from first principles — rather than memorising formulas — builds deeper understanding and allows tackling novel problems.

• Identify the relevant physical law (Newton’s laws, conservation of energy/momentum, Maxwell’s equations, etc.)
• State the mathematical form of that law as it applies here
• Check dimensions at every step: both sides of an equation must have the same units

Step-by-Step Solution

Problem Statement

A 5 kg block hangs from a string (max tension 60 N). An additional 1 kg mass is placed on it suddenly. Will the string break? ($g = 10$ m/s²)

Concepts Used

• When mass $m_1$ is placed on hanging mass $m_2$: initial jerk may create tension $> (m_1+m_2)g$; however, if placed gently and static: $T = (m_1+m_2)g$

Step-by-Step Solution

Step 1: Total weight = $(5+1) \times 10 = 60$ N = max tension exactly.

Step 2: String will just not break in static case ($T = 60$ N exactly at limit).

Step 3: If placed with any downward velocity, dynamic tension exceeds 60 N and the string breaks.

Answer

$$\boxed{\text{At limit: T} = 60\text{ N. Any dynamic loading breaks the string.}}$$

Worked Calculation

Substituting all given numerical values with their units into the derived formula:

$$\text{Numerical result} = \text{given expression substituted with values}$$

Answer

$$\boxed{\boxed{\text{At limit: T} = 60\text{ N. Any dynamic loading breaks the string.}}}$$

Physical Interpretation

The answer should be checked for dimensional consistency and physical reasonableness: is the magnitude in the expected range for this type of problem? Does the answer change in the correct direction when parameters are varied (e.g., increasing mass should increase momentum, increasing distance should decrease field strength)? These sanity checks are as important as the calculation itself.