A balanced lever has two weights on it, the first with mass #3 kg # and the second with mass #24 kg#. If the first weight is # 9 m# from the fulcrum, how far is the second weight from the fulcrum?

1 Answer
Dec 30, 2015

Answer:

# r=1.125m#

Explanation:

Let #m_1=3kg# #m_2#=24kg
Let #W_1# and #W_2# be the weights of #m_1# and #m_2# respectively.
#implies W_1=m_1*g=3*9.8=29.4N#
#implies W_2=m_2*g=24*9.8=235.2N#

Since the lever is balanced so both the torques produced by #W_1# and #W_2# should be equal.

Let the mass #m_2# be at a distance from #r# from the fulcrum.

Let #tau_1# and #tau_2# be the torques produced by #W_1# and #W_2# respectively.
#tau_1=tau_2#
#implies W_1*9=W_2*r#
#implies 29.4*9=235.2*r#
#implies r=(29.4*9)/235.2=1.125m#
#implies r=1.125m#
Hence the second weight is at a distance of 1.125m from the fulcrum.