Here's how you'd go about doing this.
In order to determine the specific heat (#"c"_("sinker"))# of a lead sinker, you will need to use a calorimeter. Let's say you have a lead sinker that weighs #"5 g"# . You'll start by placing this lead sinker in boling water for 15-20 minutes.
Place #"200 mL"# of distilled water in the calorimeter. We will assume that, after 20 minutes, the lead sinker is now at the same temperature as the boiling water, #"100"^@"C"#.
The water in the calorimeter is at room temperature, say #"25"^@"C"#. Place the hot lead sinker into the calorimeter and record, using a thermometer, the highest temperature of the mixture.
From this point on, you'll use the heat absorbed by the water to determine the specific heat of the lead sinker.
Since this is presumably a lab assignment, I'll just use the conceptual equations to solve for #"c"_("sinker")#.
The heat absorbed by the water is equal to
#q_("absorbed") = "m"_("water") * "c"_("water") * DeltaT#, where
#"c"_("water")# - the specific heat of water, #4.18# #"J"/("g" * ^@"C")#;
#DeltaT# - the difference between the final and the initial temperature of the water - will be positive in water's case, since it absorbs heat from the hot lead sinker - its final temperature will be bigger than #"25"^@"C"#.
The heat absorbed by the water must be equal to the heat given off by the sinker (in absolute terms), so
#q_("sinker") = -q_("water")#
We know that #q_("sinker")# is equal to
#q_("sinker") = "m"_("sinker") * "c"_("Sinker") * DeltaT_("sinker")#, where
#"m"_("sinker")# - the mass of the sinker - in our example, 5 g.
#DeltaT_("sinker")# - the difference btween the final and the initial temperature of the sinker - will be negative this time, since the sinker will cool off - its final temperature will be way smaller than #"100"^@"C"#.
Therefore, the value for the sinker's specific heat will be
#c_("sinker") = (-q_("water"))/("m"_("sinker") * DeltaT_("sinker")#
Usually, you'll get something around #0.125#-#0.130# #"J"/("g" * ^@"C")# for lead's specific heat.
A good example of this particular density are on this site: https://wikis.engrade.com/specificheat
